Edit Profile (opens in new tab) Vainikko, Gennadi Co-Author Distance Author ID: vainikko.gennadi Published as: Vainikko, Gennadi; Vainikko, G.; Vainikko, G. M.; Vajnikko, G. M.; Vajnikko, G.; Vajnikko, Gennadij M.; Vajnikko, Genuadi; Wainikko, G. M. more...less External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 195 Publications since 1962, including 11 Books 1 Contribution as Editor Reviewing Activity: 125 Reviews Biographic References: 9 Publications Co-Authors: 60 Co-Authors with 97 Joint Publications 901 Co-Co-Authors all top 5 Co-Authors 95 single-authored 24 Pedas, Arvet 8 Lifanov, Ivan K. 8 Saranen, Jukka 5 Karma, Otto 4 Orav-Puurand, Kerli 4 Plato, Robert 4 Vainikko, Eero 3 Diogo, Teresa 3 Hämarik, Uno 3 Krasnosel’skiĭ, Mark Aleksandrovich 3 Rutitskij, Ya. B. 3 Stet’senko, V. Ya. 3 Uba, P. R. 3 Zabreĭko, Pëtr Petrovich 2 Brunner, Hermann 2 Dement’eva, A. M. 2 Krutitskii, Pavel A. 2 Oja, Peeter 2 Pedas, A. A. 2 Rehman, Sumaira 2 Tamme, Enn 2 Turunen, Ville 1 Anfinogenov, A. Yu. 1 Bruckner, Gottfried 1 Hennebach, Ekkehard 1 Junghanns, Peter 1 Kalam, B. 1 Karpenko, L. N. 1 Kazakova, Nedyalka G. 1 Kelle, O. 1 Kivinukk, Andi 1 Kluge, Reinhard 1 Kolk, Marek 1 Kolybasova, V. V. 1 Kolybasova, Valentina 1 Kulla, V. 1 Kunisch, Karl 1 Lätt, Kaido 1 Lebedeva, Nina V. 1 Leetma, Evely 1 Lepik, Rein 1 Lima, Pedro Miguel 1 Lippus, Jüri 1 Lomp, Marika 1 Marshak, A. L. 1 Meressoo, T. Kh. 1 Miidla, Peep 1 Mijdla, P. 1 Mikhlin, Solomon Grigor’evich 1 Nevanlinna, Olavi 1 Piskarëv, S. I. 1 Poltavskij, L. N. 1 Prössdorf, Siegfried 1 Prozorov, K. V. 1 Prozorov, Konstantin 1 Roose, A. 1 Silman, A. 1 Šlapikiene, M. 1 Umanskij, J. B. 1 Veretennikov, Alexander Yu. 1 Zolk, Indrek all top 5 Serials 16 U.S.S.R. Computational Mathematics and Mathematical Physics 15 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 12 Numerical Functional Analysis and Optimization 12 Zeitschrift für Analysis und ihre Anwendungen 7 Journal of Integral Equations and Applications 6 Mathematical Modelling and Analysis 5 Proceedings of the Estonian Academy of Sciences. Physics, Mathematics 4 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 3 Journal of Computational and Applied Mathematics 3 Mathematische Nachrichten 3 SIAM Journal on Numerical Analysis 3 Sibirskiĭ Matematicheskiĭ Zhurnal 2 Journal of the Australian Mathematical Society, Series B 2 Mathematics of Computation 2 Differential Equations 2 Soviet Mathematics. Doklady 2 Izvestiya Akademii Nauk Èstonskoĭ SSR. Fizika. Matematika 2 The Journal of Analysis 2 Sbornik: Mathematics 2 Doklady Mathematics 2 Differential Equations 2 WSEAS Transactions on Mathematics 1 Applicable Analysis 1 BIT 1 Calcolo 1 Computing 1 Differentsial’nye Uravneniya 1 Functional Analysis and its Applications 1 Integral Equations and Operator Theory 1 Journal of Soviet Mathematics 1 Numerische Mathematik 1 Siberian Mathematical Journal 1 Soviet Mathematics 1 PLISKA. Studia Mathematica Bulgarica 1 Applied Numerical Mathematics 1 Journal of Complexity 1 Computational Mathematics and Mathematical Physics 1 Automation and Remote Control 1 Mathematics of the USSR, Sbornik 1 Matematicheskiĭ Sbornik 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Functional Differential Equations 1 Acta et Commentationes Universitatis Tartuensis de Mathematica 1 Computational Methods in Applied Mathematics 1 Communications on Pure and Applied Analysis 1 Lecture Notes in Mathematics 1 Mathematische Lehrbücher und Monographien. II. Abteilung: Mathematische Monographien 1 Proceedings of the Steklov Institute of Mathematics 1 Tartu Ülikooli Toimetised. Matemaatika- ja Mehhaanika-Alaseid Töid 1 Teubner-Texte zur Mathematik 1 Differential and Integral Equations and Their Applications 1 International Journal for Numerical Methods in Biomedical Engineering 1 Nonlinear Analysis. Theory, Methods & Applications 1 Springer Monographs in Mathematics all top 5 Fields 142 Numerical analysis (65-XX) 87 Integral equations (45-XX) 51 Operator theory (47-XX) 23 Partial differential equations (35-XX) 10 Fluid mechanics (76-XX) 9 Ordinary differential equations (34-XX) 5 Approximations and expansions (41-XX) 4 Real functions (26-XX) 4 Functional analysis (46-XX) 4 General topology (54-XX) 3 Potential theory (31-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Optics, electromagnetic theory (78-XX) 2 Algebraic topology (55-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 136 Publications have been cited 1,892 times in 1,272 Documents Cited by ▼ Year ▼ Periodic integral and pseudodifferential equations with numerical approximation. Zbl 0991.65125 Saranen, Jukka; Vainikko, Gennadi 117 2002 Approximate solution of operator equations. Translated by D. Louvish. Zbl 0231.41024 Krasnosel’skiĭ, M. A.; Vainikko, G. M.; Zabreiko, P. P.; Rutitskiĭ, Ya. B.; Stetsenko, V. Ya. 108 1972 Hypersingular integral equations and their applications. Zbl 1061.45001 Lifanov, I. K.; Poltavskii, L. N.; Vainikko, G. M. 94 2004 The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Zbl 0941.65136 Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi 91 1999 Multidimensional weakly singular integral equations. Zbl 0789.65097 Vainikko, Gennadi 84 1993 Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels. Zbl 0998.65134 Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi 78 2001 On the regularization of projection methods for solving ill-posed problems. Zbl 0675.65053 Plato, R.; Vainikko, G. 71 1990 Funktionalanalysis der Diskretisierungsmethoden. Zbl 0343.65023 Vainikko, Gennadi 67 1976 Approximative methods for nonlinear equations (two approaches to the convergence problem). Zbl 0401.65034 Vainikko, G. 66 1978 Galerkin’s perturbation method and the general theory of approximate methods for non-linear equations. Zbl 0213.16201 Vainikko, G. M. 56 1969 Approximate solution of operator equations. (Прибложенное решение операторных уравнений) (Näherungslösung von Operatorgleichungen.) Zbl 0194.17902 Krasnosel’skiĭ, M. A.; Vainikko, G. M.; Zabreĭko, P. P.; Rutitskiĭ, Ya. B.; Stetsenko, V. Ya. 55 1969 The properties of solutions of weakly singular integral equations. Zbl 0475.65085 Vainikko, G.; Pedas, A. 44 1981 Fast solvers of the Lippmann-Schwinger equation. Zbl 0962.65097 Vainikko, Gennadi 42 2000 Iterative procedures in ill-posed problems. (Iteratsionnye protsedury v nekorrektnykh zadachakh). Zbl 0593.65040 Vajnikko, G. M.; Veretennikov, A. Yu. 40 1986 Smoothing transformation and piecewise polynomial collocation for weakly singular Volterra integral equations. Zbl 1063.65147 Pedas, A.; Vainikko, G. 39 2004 Cordial Volterra integral equations. I. Zbl 1195.45004 Vainikko, Gennadi 39 2009 Which functions are fractionally differentiable? Zbl 1351.26018 Vainikko, Gennadi 33 2016 A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel. Zbl 0475.65084 Vainikko, G.; Uba, P. 32 1981 The discrepancy principle for a class of regularization methods. Zbl 0528.65033 Vainikko, G. M. 32 1982 Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Zbl 1133.65118 Pedas, A.; Vainikko, G. 31 2006 Cordial Volterra integral equations. II. Zbl 1194.65152 Vainikko, Gennadi 31 2010 Integral equations with diagonal and boundary singularities of the kernel. Zbl 1118.45003 Pedas, Arvet; Vainikko, Gennadi 26 2006 A spline product quasi-interpolation method for weakly singular Fredholm integral equations. Zbl 1188.65179 Vainikko, Eero; Vainikko, Gennadi 22 2008 High-order methods for Volterra integral equations with general weak singularities. Zbl 1187.65145 Kolk, Marek; Pedas, Arvet; Vainikko, Gennadi 22 2009 On symbol analysis of periodic pseudodifferential operators. Zbl 0899.47039 Turunen, V.; Vainikko, G. 21 1998 Spline collocation-interpolation method for linear and nonlinear cordial Volterra integral equations. Zbl 1215.65205 Vainikko, Gennadi 21 2011 Über die Konvergenz und Divergenz von Näherungsmethoden bei Eigenwertproblemen. Zbl 0369.65015 Vainikko, Gennadi 19 1977 On the optimality of methods for ill-posed problems. Zbl 0632.65061 Vainikko, G. 19 1987 Regular convergence of operators and approximate solution of equations. Zbl 0582.65046 Vajnikko, G. M. 18 1981 The convergence of the collokation method for nonlinear differential equations. Zbl 0154.17301 Vainikko, G. 18 1966 Superconvergence of piecewise polynomial collocations for nonlinear weakly singular integral equations. Zbl 0910.65115 Pedas, Arvet; Vainikko, Gennadi 17 1997 On the speed of convergence of approximate methods in the eigenvalue problem. Zbl 0249.65041 Vainikko, G. M. 17 1970 Nyström type methods for Fredholm integral equations with weak singularities. Zbl 1193.65226 Orav-Puurand, Kerli; Pedas, Arvet; Vainikko, Gennadi 17 2010 Trigonometric collocation methods with product integration for boundary integral equations on closed curves. Zbl 0855.65119 Saranen, J.; Vainikko, G. 15 1996 Spline collocation for cordial Volterra integral equations. Zbl 1195.65230 Vainikko, Gennadi 15 2010 Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations. Zbl 1357.65316 Diogo, T.; Lima, P. M.; Pedas, A.; Vainikko, G. 14 2017 Fast solvers of integral and pseudodifferential equations on closed curves. Zbl 0907.65138 Saranen, J.; Vainikko, G. 13 1998 Fast solvers of integral equations of the second kind: wavelet methods. Zbl 1071.65185 Vainikko, Gennadi; Kivinukk, Andi; Lippus, Jüri 12 2005 Über Konvergenzbegriffe für lineare Operatoren in der Numerischen Mathematik. Zbl 0369.65016 Vainikko, Gennadi 11 1977 The smoothness of solutions to nonlinear weakly singular integral equations. Zbl 0803.45007 Pedas, A.; Vainikko, G. 9 1994 Evaluation of the error of the Bubnov-Galerkin method in an eigenvalue problem. Zbl 0155.20202 Vainikko, G. 9 1965 Applicability of spline collocation to cordial Volterra equations. Zbl 1266.65208 Diogo, Teresa; Vainikko, Gennadi 9 2013 Convergence of the difference method when seeking the periodic solutions of ordinary differential equations. Zbl 0323.65026 Vainikko, G. M. 8 1976 Methods for the solution of weakly singular integral equations. Textbook. (Metody resheniya slabo-singulyarnykh integral’nykh uravnenij. Uchebnoe posobie). Zbl 0592.65094 Vajnikko, G.; Pedas, A.; Uba, P. 8 1984 On the regularity of solutions to integral equations with nonsmooth kernels on a union of open intervals. Zbl 1168.45003 Pedas, Arvet; Vainikko, Gennadi 8 2009 On the notion of the finite part of divergent integrals in integral equations. Zbl 1040.65109 Vainikko, G. M.; Lifanov, I. K. 8 2002 On the discretization and regularization of ill-posed problems with noncompact operators. Zbl 0759.65030 Vainikko, Gennadi 8 1992 Fast solvers of generalized airfoil equation of index 1. Zbl 1004.65145 Vainikko, Gennadi 7 2001 Error bounds of discretization methods for boundary integral equations with noisy data. Zbl 0865.65100 Bruckner, Gottfried; Prößdorf, Siegfried; Vainikko, Gennadi 7 1996 Two-grid solution of Symm’s integral equation. Zbl 0858.65135 Saranen, J.; Vainikko, G. 7 1996 On the stability and convergence of the collocation method. Zbl 0171.36503 Vainikko, G. M. 7 1966 Test examples of systems of nonlinear equations. Version 3-90. Zbl 0696.65044 Roose, A.; Kulla, V.; Lomp, M.; Meressoo, T.; Vainikko, G. 7 1990 First kind cordial Volterra integral equations. I. Zbl 1248.45002 Vainikko, Gennadi 7 2012 The critical level of discrepancy in regularization methods. Zbl 0559.65038 Vajnikko, G. M. 6 1983 Projection methods and self-regularization in ill-posed problems. Zbl 0613.65056 Vajnikko, G. M.; Khyamarik, U. A. 6 1985 Identifiability of the transmissivity coefficient in an elliptic boundary value problem. Zbl 0777.35091 Vainikko, G.; Kunisch, K. 6 1993 Asymptotic evaluations of the error of projection methods for the eigenvalue problem. Zbl 0168.13603 Vainikko, G. M. 6 1966 Fast spline quasicollocation solvers of integral equations. Zbl 1151.65103 Vainikko, G.; Zolk, I. 6 2007 On regularly consistent operators. Zbl 0388.47007 Vainikko, G. M.; Piskarev, S. I. 5 1977 Piecewise polynomial projection methods for nonlinear multidimensional weakly singular integral equations. Zbl 0957.65116 Pedas, A.; Vainikko, G. 5 2000 First kind cordial Volterra integral equations. II. Zbl 1381.45015 Vainikko, Gennadi 5 2014 Projection methods and self-regularization in ill-posed problems. Zbl 0646.65048 Vajnikko, G. M.; Khyamarik, U. A. 5 1985 Fast solvers of integral equations of the second kind: quadrature methods. Zbl 1079.65138 Vainikko, Gennadi 5 2005 A smooth solution to a linear system of singular ODEs. Zbl 1275.34014 Vainikko, Gennadi 5 2013 Central part interpolation schemes for integral equations with singularities. Zbl 1376.65158 Orav-Puurand, Kerli; Pedas, Arvet; Vainikko, Gennadi 4 2017 Über die Konvergenz und Konvergenzgeschwindigkeit der Galerkinschen Methode für abstrakte Evolutionsgleichungen. Zbl 0314.35002 Vainikko, G. M.; Oja, P. E. 4 1975 The convergence rate of approximate methods in the eigenvalue problem when the parameter appears non-linearly. Zbl 0352.65027 Vainikko, G. M.; Karma, O. O. 4 1975 On the regularization of the Ritz-Galerkin method for solving ill-posed problems. Zbl 0711.65041 Plato, Robert; Vainikko, Gennadi 4 1989 A smooth solution of a singular fractional differential equation. Zbl 1320.34011 Lätt, Kaido; Pedas, Arvet; Vainikko, Gennadi 4 2015 A fully discrete Galerkin method for integral and pseudodifferential equations on closed curves. Zbl 0832.65128 Kelle, O.; Vainikko, G. 4 1995 Numerical solution of weakly singular Volterra integral equations with change of variables. Zbl 1065.65149 Pedas, Arvet; Vainikko, Gennadi 4 2004 GMRES and discrete approximation of operators. Zbl 1067.65058 Vainikko, Gennadi 4 2004 Das Prinzip der kompakten Approximation in der Theorie der Näherungsmethoden. Zbl 0197.10802 Vainikko, G. M. 4 1969 On the convergence of the method of mechanical quadratures for integral equations with discontinuous kernels. Zbl 0229.45013 Vainikko, G. M. 4 1971 Fast wavelet solvers of periodic integral equations. Zbl 1192.65166 Vainikko, G. 4 2006 Product quasi-interpolation in logarithmically singular integral equations. Zbl 1259.65219 Vainikko, Eero; Vainikko, Gennadi 4 2012 Error estimates of the successive approximation method for ill-posed problems. Zbl 0445.65041 Vajnikko, G. M. 3 1980 Discrete compact sequences. Zbl 0287.46024 Vainikko, G. M. 3 1974 Über die Konvergenzgeschwindigkeit von Näherungsmethoden im Eigenwertproblem mit nichtlinearem Eingang des Parameters. Zbl 0339.65030 Vainikko, G. M.; Karma, O. O. 3 1974 Fast collocation solvers for integral equations on open arcs. Zbl 0976.65115 Saranen, J.; Vainikko, G. 3 1999 Modeling of aerodynamic and wave diffraction problems and extensions of Cauchy type integral operators on closed and open curves. Zbl 0993.76040 Vainikko, G. M.; Lifanov, I. K. 3 2000 Fast solvers of generalized arifoil equation of index -1. Zbl 1024.76037 Vainikko, Gennadi 3 2001 On the smoothness of the solution of multidimensional weakly singular integral equations. Zbl 0709.45011 Vajnikko, G. M. 3 1990 Identification of filtration coefficient. Zbl 0786.35150 Vainikko, G. 3 1992 Some numerical schemes for the identification of the filtration coefficient. Zbl 0813.76086 Vainikko, Eero; Vainikko, Gennadi 3 1992 Limit spectrum of discretely converging operators. Zbl 0879.47008 Nevanlinna, Olavi; Vainikko, Gennadi 3 1996 Error estimates for the cardinal spline interpolation. Zbl 1171.41005 Vainikko, Gennadi 3 2009 What is the complexity of periodic weakly singular integral equations? Zbl 1152.65122 Pedas, A.; Vainikko, G. 3 2008 Näherungsverfahren zur Lösung von Operatorgleichungen. Deutsche Übersetzung: Jurgis Szlaza. In deutscher Sprache herausgegeben von Reinhard Kluge. Zbl 0269.65001 Krasnoselski, M. A.; Wainikko, G. M.; Sabreiko, P. P.; Rutizki, J. B.; Stezenko, W. J. 2 1973 The convergence of approximate methods for solving linear and non-linear operator equations. Zbl 0306.65034 Vainikko, G. M.; Karma, O. O. 2 1975 Über die Konvergenz der Differenzenmethode im Problem der periodischen Lösungen gewöhnlicher Differentialgleichungen. Zbl 0311.65053 Vainikko, G. M. 2 1975 Über die Invarianz der Rotation bei Approximation der Vektorfelder. Zbl 0373.47036 Vainikko, Gennadi 2 1977 On the fast and fully discretized solution of integral and pseudo-differential equations on smooth curves. Zbl 1008.65098 Plato, R.; Vainikko, G. 2 2001 On the optimality of regularization methods. Zbl 0642.65040 Vainikko, Gennadi 2 1987 Tangential derivatives of solutions to nonlinear multidimensional weakly singular integral equations. Zbl 0811.45002 Pedas, A.; Vainikko, G. 2 1994 Solution of large systems arising by discretization of multidimensional weakly singular integral equations. Zbl 0808.65019 Vainikko, Gennadi 2 1992 Numerical solution of a singular and a hypersingular integral equation on an interval and the delta function. Zbl 1047.65116 Vainikko, G. M.; Lebedeva, N. V.; Lifanov, I. K. 2 2002 Speed of convergence of the method of moments for ordinary differential equations. Zbl 0165.41101 Vainikko, G. 2 1968 Regular operators. Zbl 0174.44204 Vainikko, G. M.; Umanskij, J. B. 2 1968 On the rate of convergence of certain approximation methods of Galerkin type in an eigenvalue problem. Zbl 0204.49402 Vajnikko, G. M. 2 1966 Integral equations of the third kind in \(L^p\) spaces. Zbl 1465.45001 Diogo, Teresa; Pedas, Arvet; Vainikko, Gennadi 2 2020 A quasi-fast solver for weakly singular integral equations of the second kind. Zbl 1487.65201 Rehman, Sumaira; Pedas, Arvet; Vainikko, Gennadi 1 2020 Cordial Volterra integral operators in spaces \(L^p(0,T)\). Zbl 1436.47015 Vainikko, Gennadi 2 2019 Fast solvers of weakly singular integral equations of the second kind. Zbl 1488.65755 Rehman, Sumaira; Pedas, Arvet; Vainikko, Gennadi 1 2018 Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations. Zbl 1357.65316 Diogo, T.; Lima, P. M.; Pedas, A.; Vainikko, G. 14 2017 Central part interpolation schemes for integral equations with singularities. Zbl 1376.65158 Orav-Puurand, Kerli; Pedas, Arvet; Vainikko, Gennadi 4 2017 Which functions are fractionally differentiable? Zbl 1351.26018 Vainikko, Gennadi 33 2016 A smooth solution of a singular fractional differential equation. Zbl 1320.34011 Lätt, Kaido; Pedas, Arvet; Vainikko, Gennadi 4 2015 First kind cordial Volterra integral equations. II. Zbl 1381.45015 Vainikko, Gennadi 5 2014 Applicability of spline collocation to cordial Volterra equations. Zbl 1266.65208 Diogo, Teresa; Vainikko, Gennadi 9 2013 A smooth solution to a linear system of singular ODEs. Zbl 1275.34014 Vainikko, Gennadi 5 2013 First kind cordial Volterra integral equations. I. Zbl 1248.45002 Vainikko, Gennadi 7 2012 Product quasi-interpolation in logarithmically singular integral equations. Zbl 1259.65219 Vainikko, Eero; Vainikko, Gennadi 4 2012 Spline collocation-interpolation method for linear and nonlinear cordial Volterra integral equations. Zbl 1215.65205 Vainikko, Gennadi 21 2011 Cordial Volterra integral equations. II. Zbl 1194.65152 Vainikko, Gennadi 31 2010 Nyström type methods for Fredholm integral equations with weak singularities. Zbl 1193.65226 Orav-Puurand, Kerli; Pedas, Arvet; Vainikko, Gennadi 17 2010 Spline collocation for cordial Volterra integral equations. Zbl 1195.65230 Vainikko, Gennadi 15 2010 Cordial Volterra integral equations. I. Zbl 1195.45004 Vainikko, Gennadi 39 2009 High-order methods for Volterra integral equations with general weak singularities. Zbl 1187.65145 Kolk, Marek; Pedas, Arvet; Vainikko, Gennadi 22 2009 On the regularity of solutions to integral equations with nonsmooth kernels on a union of open intervals. Zbl 1168.45003 Pedas, Arvet; Vainikko, Gennadi 8 2009 Error estimates for the cardinal spline interpolation. Zbl 1171.41005 Vainikko, Gennadi 3 2009 Cardinal approximation of functions by splines on an interval. Zbl 1168.65319 Vainikko, G. 2 2009 Central part interpolation schemes for integral equations. Zbl 1187.65149 Orav-Puurand, Kerli; Vainikko, Gennadi 2 2009 Cordial Volterra integral operators and equations. Zbl 1182.45005 Vainikko, Gennadi 1 2009 A spline product quasi-interpolation method for weakly singular Fredholm integral equations. Zbl 1188.65179 Vainikko, Eero; Vainikko, Gennadi 22 2008 What is the complexity of periodic weakly singular integral equations? Zbl 1152.65122 Pedas, A.; Vainikko, G. 3 2008 Fast spline quasicollocation solvers of integral equations. Zbl 1151.65103 Vainikko, G.; Zolk, I. 6 2007 On the best approximation of function classes from values on a uniform grid in the real line. Zbl 1120.65012 Vainikko, Gennadi 2 2007 Quasi-interpolation by splines on the uniform knot sets. Zbl 1122.65014 Leetma, E.; Vainikko, G. 2 2007 A product quasi-interpolation method for weakly singular Volterra integral equations. Zbl 1152.65395 Vainikko, Eero; Vainikko, Gennadi 1 2007 Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Zbl 1133.65118 Pedas, A.; Vainikko, G. 31 2006 Integral equations with diagonal and boundary singularities of the kernel. Zbl 1118.45003 Pedas, Arvet; Vainikko, Gennadi 26 2006 Fast wavelet solvers of periodic integral equations. Zbl 1192.65166 Vainikko, G. 4 2006 Piecewise polynomial approximations for integral equations with diagonal and boundary singularities. Zbl 1192.65164 Pedas, A.; Vainikko, G. 2 2006 Fast solvers of integral equations of the second kind: wavelet methods. Zbl 1071.65185 Vainikko, Gennadi; Kivinukk, Andi; Lippus, Jüri 12 2005 Fast solvers of integral equations of the second kind: quadrature methods. Zbl 1079.65138 Vainikko, Gennadi 5 2005 Boundary singularities of solutions to integral equations of the second kind. Zbl 1205.45002 Pedas, Arvet; Vainikko, Gennadi 1 2005 Hypersingular integral equations and their applications. Zbl 1061.45001 Lifanov, I. K.; Poltavskii, L. N.; Vainikko, G. M. 94 2004 Smoothing transformation and piecewise polynomial collocation for weakly singular Volterra integral equations. Zbl 1063.65147 Pedas, A.; Vainikko, G. 39 2004 Numerical solution of weakly singular Volterra integral equations with change of variables. Zbl 1065.65149 Pedas, Arvet; Vainikko, Gennadi 4 2004 GMRES and discrete approximation of operators. Zbl 1067.65058 Vainikko, Gennadi 4 2004 Periodic integral and pseudodifferential equations with numerical approximation. Zbl 0991.65125 Saranen, Jukka; Vainikko, Gennadi 117 2002 On the notion of the finite part of divergent integrals in integral equations. Zbl 1040.65109 Vainikko, G. M.; Lifanov, I. K. 8 2002 Numerical solution of a singular and a hypersingular integral equation on an interval and the delta function. Zbl 1047.65116 Vainikko, G. M.; Lebedeva, N. V.; Lifanov, I. K. 2 2002 Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels. Zbl 0998.65134 Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi 78 2001 Fast solvers of generalized airfoil equation of index 1. Zbl 1004.65145 Vainikko, Gennadi 7 2001 Fast solvers of generalized arifoil equation of index -1. Zbl 1024.76037 Vainikko, Gennadi 3 2001 On the fast and fully discretized solution of integral and pseudo-differential equations on smooth curves. Zbl 1008.65098 Plato, R.; Vainikko, G. 2 2001 Fast solution of periodic integral equations by GMRES. Zbl 1026.65127 Plato, R.; Vainikko, G. 1 2001 Fast solvers of the Lippmann-Schwinger equation. Zbl 0962.65097 Vainikko, Gennadi 42 2000 Piecewise polynomial projection methods for nonlinear multidimensional weakly singular integral equations. Zbl 0957.65116 Pedas, A.; Vainikko, G. 5 2000 Modeling of aerodynamic and wave diffraction problems and extensions of Cauchy type integral operators on closed and open curves. Zbl 0993.76040 Vainikko, G. M.; Lifanov, I. K. 3 2000 Generalization and use of the theory of pseudodifferential operators in the modeling of some problems in mechanics. Zbl 1137.76322 Vainikko, G. M.; Lifanov, I. K. 1 2000 The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Zbl 0941.65136 Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi 91 1999 Fast collocation solvers for integral equations on open arcs. Zbl 0976.65115 Saranen, J.; Vainikko, G. 3 1999 An integral operator representation of classical periodic pseudodifferential operators. Zbl 0939.47042 Vainikko, G. 1 1999 On symbol analysis of periodic pseudodifferential operators. Zbl 0899.47039 Turunen, V.; Vainikko, G. 21 1998 Fast solvers of integral and pseudodifferential equations on closed curves. Zbl 0907.65138 Saranen, J.; Vainikko, G. 13 1998 Superconvergence of piecewise polynomial collocations for nonlinear weakly singular integral equations. Zbl 0910.65115 Pedas, Arvet; Vainikko, Gennadi 17 1997 Trigonometric Galerkin fast solvers for periodic integral equation of the first kind. Zbl 1040.65108 Vainikko, G. 1 1997 Trigonometric collocation methods with product integration for boundary integral equations on closed curves. Zbl 0855.65119 Saranen, J.; Vainikko, G. 15 1996 Error bounds of discretization methods for boundary integral equations with noisy data. Zbl 0865.65100 Bruckner, Gottfried; Prößdorf, Siegfried; Vainikko, Gennadi 7 1996 Two-grid solution of Symm’s integral equation. Zbl 0858.65135 Saranen, J.; Vainikko, G. 7 1996 Limit spectrum of discretely converging operators. Zbl 0879.47008 Nevanlinna, Olavi; Vainikko, Gennadi 3 1996 Two-grid solution of boundary integral equations on closed curves. Zbl 0882.65105 Saranen, J.; Vainikko, G. 1 1996 A fully discrete Galerkin method for integral and pseudodifferential equations on closed curves. Zbl 0832.65128 Kelle, O.; Vainikko, G. 4 1995 Weakly singular integral equations with operator-valued kernels and an application to radiation transfer problems. Zbl 0828.45012 Hennebach, E.; Junghanns, P.; Vainikko, G. 1 1995 The smoothness of solutions to nonlinear weakly singular integral equations. Zbl 0803.45007 Pedas, A.; Vainikko, G. 9 1994 Tangential derivatives of solutions to nonlinear multidimensional weakly singular integral equations. Zbl 0811.45002 Pedas, A.; Vainikko, G. 2 1994 Multidimensional weakly singular integral equations. Zbl 0789.65097 Vainikko, Gennadi 84 1993 Identifiability of the transmissivity coefficient in an elliptic boundary value problem. Zbl 0777.35091 Vainikko, G.; Kunisch, K. 6 1993 On the discretization and regularization of ill-posed problems with noncompact operators. Zbl 0759.65030 Vainikko, Gennadi 8 1992 Identification of filtration coefficient. Zbl 0786.35150 Vainikko, G. 3 1992 Some numerical schemes for the identification of the filtration coefficient. Zbl 0813.76086 Vainikko, Eero; Vainikko, Gennadi 3 1992 Solution of large systems arising by discretization of multidimensional weakly singular integral equations. Zbl 0808.65019 Vainikko, Gennadi 2 1992 Piecewise constant approximation of the solution of multi-dimensional weakly singular integral equations. Zbl 0736.65089 Vajnikko, G. M. 2 1991 On the regularization of projection methods for solving ill-posed problems. Zbl 0675.65053 Plato, R.; Vainikko, G. 71 1990 Test examples of systems of nonlinear equations. Version 3-90. Zbl 0696.65044 Roose, A.; Kulla, V.; Lomp, M.; Meressoo, T.; Vainikko, G. 7 1990 On the smoothness of the solution of multidimensional weakly singular integral equations. Zbl 0709.45011 Vajnikko, G. M. 3 1990 Integral equations of an interior-exterior problem and their approximate solution. Zbl 0712.65100 Vainikko, Gennadi 1 1990 Some collocation methods for solving multi-dimensional weakly singular integral equations. Zbl 0721.65097 Vajnikko, G. M. 1 1990 Convergence rate of a modified cubature formula method for multidimensional weakly singular integral equations. Zbl 0801.65130 Vainikko, Gennadi; Pedas, Arvet 1 1990 On the regularization of the Ritz-Galerkin method for solving ill-posed problems. Zbl 0711.65041 Plato, Robert; Vainikko, Gennadi 4 1989 On the smoothness of multi-dimensional weakly singular integral equations. Zbl 0693.45005 Vajnikko, G. M. 2 1989 On the optimality of methods for ill-posed problems. Zbl 0632.65061 Vainikko, G. 19 1987 On the optimality of regularization methods. Zbl 0642.65040 Vainikko, Gennadi 2 1987 Iterative procedures in ill-posed problems. (Iteratsionnye protsedury v nekorrektnykh zadachakh). Zbl 0593.65040 Vajnikko, G. M.; Veretennikov, A. Yu. 40 1986 Projection methods and self-regularization in ill-posed problems. Zbl 0613.65056 Vajnikko, G. M.; Khyamarik, U. A. 6 1985 Projection methods and self-regularization in ill-posed problems. Zbl 0646.65048 Vajnikko, G. M.; Khyamarik, U. A. 5 1985 Error estimates of regularization methods for normally solvable problems. Zbl 0589.65050 Vajnikko, G. M. 1 1985 Methods for the solution of weakly singular integral equations. Textbook. (Metody resheniya slabo-singulyarnykh integral’nykh uravnenij. Uchebnoe posobie). Zbl 0592.65094 Vajnikko, G.; Pedas, A.; Uba, P. 8 1984 The critical level of discrepancy in regularization methods. Zbl 0559.65038 Vajnikko, G. M. 6 1983 The discrepancy principle for a class of regularization methods. Zbl 0528.65033 Vainikko, G. M. 32 1982 Discrepancy principle for a class of iterative methods. Zbl 0598.65033 Vajnikko, G. M. 1 1982 The properties of solutions of weakly singular integral equations. Zbl 0475.65085 Vainikko, G.; Pedas, A. 44 1981 A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel. Zbl 0475.65084 Vainikko, G.; Uba, P. 32 1981 Regular convergence of operators and approximate solution of equations. Zbl 0582.65046 Vajnikko, G. M. 18 1981 Error estimates of the successive approximation method for ill-posed problems. Zbl 0445.65041 Vajnikko, G. M. 3 1980 Approximative methods for nonlinear equations (two approaches to the convergence problem). Zbl 0401.65034 Vainikko, G. 66 1978 Über die Konvergenz und Divergenz von Näherungsmethoden bei Eigenwertproblemen. Zbl 0369.65015 Vainikko, Gennadi 19 1977 ...and 36 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,486 Authors 42 Vainikko, Gennadi 30 Pedas, Arvet 30 Piskarëv, S. I. 29 Nelakanti, Gnaneshwar 18 Tamme, Enn 16 Pereverzev, Sergei V. 15 Stynes, Martin Joseph 14 Brunner, Hermann 14 Xu, Yuesheng 11 Cai, Haotao 11 Domínguez, Víctor 11 Krutitskii, Pavel A. 10 Allouch, Chafik 10 Diogo, Teresa 10 Grigorieff, Rolf Dieter 10 Mandal, Moumita 10 Occorsio, Donatella 10 Tahrichi, Mohamed 9 Assari, Pouria 9 De Bonis, Maria Carmela 9 Sayas, Francisco-Javier 8 Arrieta, José M. 8 Das, Payel 8 Hämarik, Uno 8 Huang, Chengming 8 Kant, Kapil 8 Lechleiter, Armin 8 Sbibih, Driss 8 Vondřejc, Jaroslav 8 Yang, Zhanwen 8 Zhang, Xiaoping 7 Boĭkov, Il’ya Vladimirovich 7 Chen, Zhongying 7 Dehghan Takht Fooladi, Mehdi 7 Grammont, Laurence 7 Mustapha, Kassem 7 Panigrahi, Bijaya Laxmi 7 Plato, Robert 7 Song, Huiming 7 Tuan, Hoang The 7 Vikerpuur, Mikk 6 Băleanu, Dumitru I. 6 Cardona, Duván 6 Eshkuvatov, Zainidin K. 6 Fermo, Luisa 6 Ganesh, Mahadevan 6 Kangro, Urve 6 Kokurin, Mikhail Mikhailovich 6 Kulkarni, Rekha P. 6 Maleknejad, Khosrow 6 Monegato, Giovanni 6 Nair, M. Thamban 6 Nguyen, Dinh Liem 6 Siltanen, Samuli 6 Tautenhahn, Ulrich 5 Bruno, Oscar P. 5 Gao, Wenwu 5 Hohage, Thorsten 5 Kaltenbacher, Barbara 5 Kaneko, Hideaki 5 Karchevskii, Evgenii Mikhailovich 5 Khalilov, Elnur H. 5 Klibanov, Michael V. 5 Kokurin, Mikhail Yur’evich 5 Kumar, Vishvesh 5 Li, Xiaoxiao 5 Liang, Hui 5 Lima, Pedro Miguel 5 Mathé, Peter 5 Mueller, Jennifer L. 5 Nik Long, N. M. A. 5 Palm, Reimo 5 Pereira, Marcone Corrêa 5 Popkov, Yuriĭ Solomonovich 5 Prössdorf, Siegfried 5 Rapún, María-Luisa 5 Raus, Toomas 5 Reddien, George W. jun. 5 Semenova, Evgeniya V. 5 Setukha, Alexey V. 5 Shiri, Babak 5 Sloan, Ian Hugh 5 Solodky, Sergei G. 5 Turunen, Ville 5 Włodarczyk, Kazimierz 5 Wu, Guocheng 5 Xiao, Yu 5 Yang, Fan 5 Yang, Hongqi 5 Zeman, Jan 5 Zhao, Zhenyu 5 Zhukovskiĭ, Evgeniĭ Semenovich 4 Beyn, Wolf-Jürgen 4 Boykova, A. I. 4 Bujanda, Blanca 4 Cao, Yanzhao 4 Chakraborty, Samiran 4 Chen, Yanping 4 Gunzburger, Max D. 4 Hanke-Bourgeois, Martin ...and 1,386 more Authors all top 5 Cited in 260 Serials 92 Journal of Computational and Applied Mathematics 61 Applied Numerical Mathematics 58 Numerical Functional Analysis and Optimization 53 Journal of Integral Equations and Applications 38 Applied Mathematics and Computation 34 Numerische Mathematik 33 Journal of Mathematical Analysis and Applications 25 Journal of Scientific Computing 23 Mathematics of Computation 22 Computers & Mathematics with Applications 21 Journal of Mathematical Sciences (New York) 20 Journal of Computational Physics 19 International Journal of Computer Mathematics 18 Numerical Algorithms 18 Differential Equations 17 Computational Mathematics and Mathematical Physics 16 Ukrainian Mathematical Journal 16 Integral Equations and Operator Theory 16 Journal of Inverse and Ill-Posed Problems 15 Inverse Problems 15 Mathematical Modelling and Analysis 14 Zeitschrift für Analysis und ihre Anwendungen 14 Computational and Applied Mathematics 14 Advances in Computational Mathematics 12 BIT 12 Doklady Mathematics 10 Journal of Applied Mathematics and Mechanics 10 Mathematical Notes 10 Computing 10 Linear Algebra and its Applications 10 Computational Methods in Applied Mathematics 9 Calcolo 9 Russian Mathematics 8 Applicable Analysis 8 Mathematical Methods in the Applied Sciences 8 Mathematics and Computers in Simulation 8 SIAM Journal on Numerical Analysis 8 Journal of Complexity 8 Journal of Applied Mathematics and Computing 8 Inverse Problems in Science and Engineering 7 Journal of Differential Equations 7 Mathematische Nachrichten 7 SIAM Journal on Scientific Computing 7 Fractional Calculus & Applied Analysis 6 Computer Methods in Applied Mechanics and Engineering 6 Communications in Nonlinear Science and Numerical Simulation 6 Discrete and Continuous Dynamical Systems. Series B 6 Journal of Pseudo-Differential Operators and Applications 5 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 5 Applied Mathematics Letters 5 ETNA. Electronic Transactions on Numerical Analysis 5 Lobachevskii Journal of Mathematics 5 SIAM Journal on Imaging Sciences 5 Ufimskiĭ Matematicheskiĭ Zhurnal 5 International Journal of Applied and Computational Mathematics 4 Wave Motion 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Systems & Control Letters 4 Numerical Methods for Partial Differential Equations 4 SIAM Journal on Applied Mathematics 4 The Journal of Analysis 4 Engineering Analysis with Boundary Elements 4 Abstract and Applied Analysis 4 Journal of Applied Mathematics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Fixed Point Theory and Applications 4 Advances in Difference Equations 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Proceedings of the Steklov Institute of Mathematics 4 Journal of Fixed Point Theory and Applications 4 Inverse Problems and Imaging 4 Nonlinear Analysis. Theory, Methods & Applications 3 Chaos, Solitons and Fractals 3 Prikladnaya Matematika i Mekhanika 3 Journal of Optimization Theory and Applications 3 Journal of Soviet Mathematics 3 Siberian Mathematical Journal 3 Acta Applicandae Mathematicae 3 Physica D 3 Journal of Elasticity 3 Cybernetics and Systems Analysis 3 Fractals 3 Filomat 3 The Journal of Fourier Analysis and Applications 3 Matematychni Metody ta Fizyko-Mekhanichni Polya 3 Analysis and Applications (Singapore) 3 International Journal of Computational Methods 3 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 3 Advances in Applied Mathematics and Mechanics 3 Mathematical Sciences 3 Vestnik Rossiĭskikh Universitetov. Matematika 2 Journal of Engineering Mathematics 2 Journal of Mathematical Physics 2 International Journal for Numerical Methods in Engineering 2 Journal of Approximation Theory 2 Journal of Functional Analysis 2 Journal of Mathematical Economics 2 Journal of Multivariate Analysis 2 Mathematische Zeitschrift ...and 160 more Serials all top 5 Cited in 46 Fields 915 Numerical analysis (65-XX) 480 Integral equations (45-XX) 292 Partial differential equations (35-XX) 255 Operator theory (47-XX) 150 Ordinary differential equations (34-XX) 59 Mechanics of deformable solids (74-XX) 57 Optics, electromagnetic theory (78-XX) 56 Approximations and expansions (41-XX) 52 Real functions (26-XX) 43 Fluid mechanics (76-XX) 31 Harmonic analysis on Euclidean spaces (42-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 23 Systems theory; control (93-XX) 22 Dynamical systems and ergodic theory (37-XX) 21 Functional analysis (46-XX) 19 General topology (54-XX) 18 Potential theory (31-XX) 18 Global analysis, analysis on manifolds (58-XX) 18 Operations research, mathematical programming (90-XX) 18 Biology and other natural sciences (92-XX) 16 Probability theory and stochastic processes (60-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 14 Functions of a complex variable (30-XX) 13 Statistics (62-XX) 11 Information and communication theory, circuits (94-XX) 9 Quantum theory (81-XX) 8 Computer science (68-XX) 7 Special functions (33-XX) 7 Statistical mechanics, structure of matter (82-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Abstract harmonic analysis (43-XX) 5 Integral transforms, operational calculus (44-XX) 5 Mechanics of particles and systems (70-XX) 5 Geophysics (86-XX) 4 Difference and functional equations (39-XX) 2 History and biography (01-XX) 2 Topological groups, Lie groups (22-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Number theory (11-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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