Yang, Zhengfeng; Zhao, Hanrui; Zhi, Lihong VerifyRealRoots: a Matlab package for computing verified real solutions of polynomials systems of equations and inequalities. (English) Zbl 07741549 J. Syst. Sci. Complex. 36, No. 2, 866-883 (2023). MSC: 65-XX PDFBibTeX XMLCite \textit{Z. Yang} et al., J. Syst. Sci. Complex. 36, No. 2, 866--883 (2023; Zbl 07741549) Full Text: DOI
Rump, Siegfried M.; Lange, Marko Fast computation of error bounds for all eigenpairs of a Hermitian and all singular pairs of a rectangular matrix with emphasis on eigen- and singular value clusters. (English) Zbl 1517.65025 J. Comput. Appl. Math. 434, Article ID 115332, 22 p. (2023). MSC: 65F15 65G20 PDFBibTeX XMLCite \textit{S. M. Rump} and \textit{M. Lange}, J. Comput. Appl. Math. 434, Article ID 115332, 22 p. (2023; Zbl 1517.65025) Full Text: DOI
Cheng, Jin-San; Wen, Junyi; Zhang, Bingwei Certified numerical real root isolation for bivariate nonlinear systems. (English) Zbl 1505.65201 J. Symb. Comput. 114, 149-171 (2023). MSC: 65H10 PDFBibTeX XMLCite \textit{J.-S. Cheng} et al., J. Symb. Comput. 114, 149--171 (2023; Zbl 1505.65201) Full Text: DOI
Miyajima, Shinya Fast verified computation for positive solutions to \(\mathcal{M} \)-tensor multi-linear systems and Perron vectors of a kind of weakly irreducible nonnegative tensors. (English) Zbl 1490.65085 J. Comput. Appl. Math. 406, Article ID 113930, 15 p. (2022). MSC: 65F99 15A69 65F10 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Comput. Appl. Math. 406, Article ID 113930, 15 p. (2022; Zbl 1490.65085) Full Text: DOI
Constantineau, Kevin; García-Azpeitia, Carlos; Lessard, Jean-Philippe Spatial relative equilibria and periodic solutions of the Coulomb \((n+1)\)-body problem. (English) Zbl 1493.70056 Qual. Theory Dyn. Syst. 21, No. 1, Paper No. 3, 19 p. (2022). MSC: 70F10 65G40 47H11 34C25 37G40 PDFBibTeX XMLCite \textit{K. Constantineau} et al., Qual. Theory Dyn. Syst. 21, No. 1, Paper No. 3, 19 p. (2022; Zbl 1493.70056) Full Text: DOI arXiv
Duff, Timothy; Hein, Nickolas; Sottile, Frank Certification for polynomial systems via square subsystems. (English) Zbl 1476.14103 J. Symb. Comput. 109, 367-385 (2022). Reviewer: Juan C. Migliore (Notre Dame) MSC: 14Q65 65G20 65H10 PDFBibTeX XMLCite \textit{T. Duff} et al., J. Symb. Comput. 109, 367--385 (2022; Zbl 1476.14103) Full Text: DOI arXiv
Menini, Laura; Possieri, Corrado; Tornambè, Antonio A dynamical interval Newton method. (English) Zbl 1466.93110 Eur. J. Control 59, 290-300 (2021). MSC: 93C85 93B53 93C10 49M15 PDFBibTeX XMLCite \textit{L. Menini} et al., Eur. J. Control 59, 290--300 (2021; Zbl 1466.93110) Full Text: DOI
Moczurad, Małgorzata; Zgliczyński, Piotr Central configurations in the spatial \(n\)-body problem for \(n=5,6\) with equal masses. (English) Zbl 1470.70018 Celest. Mech. Dyn. Astron. 132, No. 11-12, Paper No. 56, 27 p. (2020). MSC: 70F10 PDFBibTeX XMLCite \textit{M. Moczurad} and \textit{P. Zgliczyński}, Celest. Mech. Dyn. Astron. 132, No. 11--12, Paper No. 56, 27 p. (2020; Zbl 1470.70018) Full Text: DOI arXiv
Frommer, Andreas; Hashemi, Behnam Computing enclosures for the matrix exponential. (English) Zbl 1459.65056 SIAM J. Matrix Anal. Appl. 41, No. 4, 1674-1703 (2020). MSC: 65F60 65G20 15A16 PDFBibTeX XMLCite \textit{A. Frommer} and \textit{B. Hashemi}, SIAM J. Matrix Anal. Appl. 41, No. 4, 1674--1703 (2020; Zbl 1459.65056) Full Text: DOI
Burr, Michael; Gao, Shuhong; Tsigaridas, Elias The complexity of subdivision for diameter-distance tests. (English) Zbl 1444.68274 J. Symb. Comput. 101, 1-27 (2020). MSC: 68U05 14Q20 68W30 68W40 PDFBibTeX XMLCite \textit{M. Burr} et al., J. Symb. Comput. 101, 1--27 (2020; Zbl 1444.68274) Full Text: DOI arXiv
Moczurad, Małgorzata; Zgliczyński, Piotr Central configurations in planar \(n\)-body problem with equal masses for \(n=5,6,7\). (English) Zbl 1451.70024 Celest. Mech. Dyn. Astron. 131, No. 10, Paper No. 46, 28 p. (2019). MSC: 70F10 PDFBibTeX XMLCite \textit{M. Moczurad} and \textit{P. Zgliczyński}, Celest. Mech. Dyn. Astron. 131, No. 10, Paper No. 46, 28 p. (2019; Zbl 1451.70024) Full Text: DOI arXiv
Hou, Guoliang; Zhang, Shugong An improved verification algorithm for nonlinear systems of equations based on Krawczyk operator. (English) Zbl 1416.65143 J. Comput. Appl. Math. 359, 145-152 (2019). MSC: 65H10 65G20 PDFBibTeX XMLCite \textit{G. Hou} and \textit{S. Zhang}, J. Comput. Appl. Math. 359, 145--152 (2019; Zbl 1416.65143) Full Text: DOI
Hladík, Milan; Skalna, Iwona Relations between various methods for solving linear interval and parametric equations. (English) Zbl 1436.65059 Linear Algebra Appl. 574, 1-21 (2019). Reviewer: Karel Zimmermann (Praha) MSC: 65G40 15A06 15Bxx PDFBibTeX XMLCite \textit{M. Hladík} and \textit{I. Skalna}, Linear Algebra Appl. 574, 1--21 (2019; Zbl 1436.65059) Full Text: DOI
Wang, Yu; Xia, Bican A hybrid procedure for finding real points on a real algebraic set. (English) Zbl 1407.65057 J. Syst. Sci. Complex. 32, No. 1, 185-204 (2019). MSC: 65H10 65H20 14P05 68W30 PDFBibTeX XMLCite \textit{Y. Wang} and \textit{B. Xia}, J. Syst. Sci. Complex. 32, No. 1, 185--204 (2019; Zbl 1407.65057) Full Text: DOI
Haqiri, Tayyebe; Mohseni Moghadam, Mahmoud; Rivaz, Azim The united stable solution set of interval continuous-time algebraic Riccati equation and verified numerical computation of its outer estimation. (English) Zbl 1424.65051 Turk. J. Math. 42, No. 3, 1130-1155 (2018). MSC: 65F30 15A24 65G30 PDFBibTeX XMLCite \textit{T. Haqiri} et al., Turk. J. Math. 42, No. 3, 1130--1155 (2018; Zbl 1424.65051) Full Text: DOI
Rump, Siegfried M. Mathematically rigorous global optimization in floating-point arithmetic. (English) Zbl 1398.65093 Optim. Methods Softw. 33, No. 4-6, 771-798 (2018). MSC: 65G20 65H20 65K05 PDFBibTeX XMLCite \textit{S. M. Rump}, Optim. Methods Softw. 33, No. 4--6, 771--798 (2018; Zbl 1398.65093) Full Text: DOI
Li, Zhe; Wan, Baocheng; Gao, Ruimei Verified error bounds for eigenvalues of geometric multiplicity \(q\) and corresponding invariant subspaces. (English) Zbl 1384.65027 Numer. Algorithms 77, No. 2, 631-652 (2018). Reviewer: Anton Iliev (Plovdiv) MSC: 65F15 65G20 PDFBibTeX XMLCite \textit{Z. Li} et al., Numer. Algorithms 77, No. 2, 631--652 (2018; Zbl 1384.65027) Full Text: DOI
Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\). (English) Zbl 1415.65121 J. Symb. Comput. 84, 147-171 (2018). MSC: 65H99 12D10 PDFBibTeX XMLCite \textit{T. Ayyildiz Akoglu} et al., J. Symb. Comput. 84, 147--171 (2018; Zbl 1415.65121) Full Text: DOI arXiv
Horáček, Jaroslav; Hladík, Milan; Černý, Michal Interval linear algebra and computational complexity. (English) Zbl 06979547 Bebiano, Natália (ed.), Applied and computational matrix analysis. MAT-TRIAD, Coimbra, Portugal, September 7–11, 2015. Selected, revised contributions. Cham: Springer. Springer Proc. Math. Stat. 192, 37-66 (2017). MSC: 65Y20 65G30 PDFBibTeX XMLCite \textit{J. Horáček} et al., Springer Proc. Math. Stat. 192, 37--66 (2017; Zbl 06979547) Full Text: DOI arXiv
Singh, Sukhjit; Gupta, D. K.; Roy, Falguni Higher order multi-step interval iterative methods for solving nonlinear equations in \(\mathbb R^n\). (English) Zbl 1385.65040 S\(\vec{\text{e}}\)MA J. 74, No. 2, 133-146 (2017). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 65H10 65G40 65Y20 PDFBibTeX XMLCite \textit{S. Singh} et al., S\(\vec{\text{e}}\)MA J. 74, No. 2, 133--146 (2017; Zbl 1385.65040) Full Text: DOI
Kapela, Tomasz; Simó, Carles Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems. (English) Zbl 1412.70024 Nonlinearity 30, No. 3, 965-986 (2017). MSC: 70H08 70F10 37J40 37J25 PDFBibTeX XMLCite \textit{T. Kapela} and \textit{C. Simó}, Nonlinearity 30, No. 3, 965--986 (2017; Zbl 1412.70024) Full Text: DOI arXiv
Imbach, Rémi; Moroz, Guillaume; Pouget, Marc A certified numerical algorithm for the topology of resultant and discriminant curves. (English) Zbl 1354.14052 J. Symb. Comput. 80, Part 2, 285-306 (2017). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 14H50 14H20 14P05 14Q05 65Y04 PDFBibTeX XMLCite \textit{R. Imbach} et al., J. Symb. Comput. 80, Part 2, 285--306 (2017; Zbl 1354.14052) Full Text: DOI arXiv HAL
Castelli, Roberto; Teismann, Holger Rigorous numerics for NLS: bound states, spectra, and controllability. (English) Zbl 1417.65193 Physica D 334, 158-173 (2016). MSC: 65N25 93B05 35Q55 93C20 65L15 PDFBibTeX XMLCite \textit{R. Castelli} and \textit{H. Teismann}, Physica D 334, 158--173 (2016; Zbl 1417.65193) Full Text: DOI arXiv Link
Walawska, Irmina; Wilczak, Daniel An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs. (English) Zbl 1410.65259 Appl. Math. Comput. 291, 303-322 (2016). MSC: 65L05 65G20 68W40 PDFBibTeX XMLCite \textit{I. Walawska} and \textit{D. Wilczak}, Appl. Math. Comput. 291, 303--322 (2016; Zbl 1410.65259) Full Text: DOI arXiv
Araya, Ignacio; Reyes, Victor Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects. (English) Zbl 1353.90113 J. Glob. Optim. 65, No. 4, 837-866 (2016). MSC: 90C26 90C57 PDFBibTeX XMLCite \textit{I. Araya} and \textit{V. Reyes}, J. Glob. Optim. 65, No. 4, 837--866 (2016; Zbl 1353.90113) Full Text: DOI
Hoffman, Neil; Ichihara, Kazuhiro; Kashiwagi, Masahide; Masai, Hidetoshi; Oishi, Shin’ichi; Takayasu, Akitoshi Verified computations for hyperbolic 3-manifolds. (English) Zbl 1337.57044 Exp. Math. 25, No. 1, 66-78 (2016). MSC: 57M50 65G40 PDFBibTeX XMLCite \textit{N. Hoffman} et al., Exp. Math. 25, No. 1, 66--78 (2016; Zbl 1337.57044) Full Text: DOI arXiv
Koupaei, J. Alikhani; Hosseini, S. M. M. A new hybrid algorithm based on chaotic maps for solving systems of nonlinear equations. (English) Zbl 1355.49028 Chaos Solitons Fractals 81, Part A, 233-245 (2015). MSC: 49M30 49K10 37N40 37E05 PDFBibTeX XMLCite \textit{J. A. Koupaei} and \textit{S. M. M. Hosseini}, Chaos Solitons Fractals 81, Part A, 233--245 (2015; Zbl 1355.49028) Full Text: DOI
Li, Zhe; Sang, Haifeng Verified error bounds for singular solutions of nonlinear systems. (English) Zbl 1328.65121 Numer. Algorithms 70, No. 2, 309-331 (2015). Reviewer: Anton Iliev (Plovdiv) MSC: 65H10 13P05 11A05 PDFBibTeX XMLCite \textit{Z. Li} and \textit{H. Sang}, Numer. Algorithms 70, No. 2, 309--331 (2015; Zbl 1328.65121) Full Text: DOI
Miyajima, Shinya Fast verified computation for solutions of continuous-time algebraic Riccati equations. (English) Zbl 1329.65093 Japan J. Ind. Appl. Math. 32, No. 2, 529-544 (2015). Reviewer: Michael Jung (Dresden) MSC: 65G20 15A24 65F30 93C05 65G30 PDFBibTeX XMLCite \textit{S. Miyajima}, Japan J. Ind. Appl. Math. 32, No. 2, 529--544 (2015; Zbl 1329.65093) Full Text: DOI
Bozóki, Sándor; Lee, Tsung-Lin; Rónyai, Lajos Seven mutually touching infinite cylinders. (English) Zbl 1310.65022 Comput. Geom. 48, No. 2, 87-93 (2015). MSC: 65D18 65H20 PDFBibTeX XMLCite \textit{S. Bozóki} et al., Comput. Geom. 48, No. 2, 87--93 (2015; Zbl 1310.65022) Full Text: DOI arXiv
Miyajima, Shinya Fast enclosure for a matrix inverse square root. (English) Zbl 1305.65133 Linear Algebra Appl. 467, 116-135 (2015). MSC: 65F30 65G30 65F05 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Linear Algebra Appl. 467, 116--135 (2015; Zbl 1305.65133) Full Text: DOI
Barrio, Roberto; Rodríguez, Marcos Systematic computer assisted proofs of periodic orbits of Hamiltonian systems. (English) Zbl 1510.37097 Commun. Nonlinear Sci. Numer. Simul. 19, No. 8, 2660-2675 (2014). MSC: 37J46 37M25 68V05 PDFBibTeX XMLCite \textit{R. Barrio} and \textit{M. Rodríguez}, Commun. Nonlinear Sci. Numer. Simul. 19, No. 8, 2660--2675 (2014; Zbl 1510.37097) Full Text: DOI
Turgut, Oguz Emrah; Turgut, Mert Sinan; Coban, Mustafa Turhan Chaotic quantum behaved particle swarm optimization algorithm for solving nonlinear system of equations. (English) Zbl 1362.65058 Comput. Math. Appl. 68, No. 4, 508-530 (2014). MSC: 65H10 PDFBibTeX XMLCite \textit{O. E. Turgut} et al., Comput. Math. Appl. 68, No. 4, 508--530 (2014; Zbl 1362.65058) Full Text: DOI
Adam, S. P.; Karras, D. A.; Magoulas, G. D.; Vrahatis, M. N. Solving the linear interval tolerance problem for weight initialization of neural networks. (English) Zbl 1323.92012 Neural Netw. 54, 17-37 (2014). MSC: 92B20 68T05 PDFBibTeX XMLCite \textit{S. P. Adam} et al., Neural Netw. 54, 17--37 (2014; Zbl 1323.92012) Full Text: DOI Link
Li, Zhe; Liu, Qi A heuristic verification of the degree of the approximate GCD of two univariate polynomials. (English) Zbl 1302.68333 Numer. Algorithms 67, No. 2, 319-334 (2014). MSC: 68W30 65H04 13P05 11A05 PDFBibTeX XMLCite \textit{Z. Li} and \textit{Q. Liu}, Numer. Algorithms 67, No. 2, 319--334 (2014; Zbl 1302.68333) Full Text: DOI
Frommer, Andreas; Hashemi, Behnam; Sablik, Thomas Computing enclosures for the inverse square root and the sign function of a matrix. (English) Zbl 1293.65071 Linear Algebra Appl. 456, 199-213 (2014). MSC: 65F30 15A24 65G30 65G20 PDFBibTeX XMLCite \textit{A. Frommer} et al., Linear Algebra Appl. 456, 199--213 (2014; Zbl 1293.65071) Full Text: DOI
Garloff, Jürgen; Popova, Evgenija D.; Smith, Andrew P. Solving linear systems with polynomial parameter dependency with application to the verified solution of problems in structural mechanics. (English) Zbl 1311.65033 Chinchuluun, Altannar (ed.) et al., Optimization, simulation, and control. New York, NY: Springer (ISBN 978-1-4614-5130-3/hbk; 978-1-4614-5131-0/ebook). Springer Optimization and Its Applications 76, 301-318 (2013). MSC: 65F10 65G30 65G20 74S05 PDFBibTeX XMLCite \textit{J. Garloff} et al., Springer Optim. Appl. 76, 301--318 (2013; Zbl 1311.65033) Full Text: DOI
Miyajima, Shinya Fast enclosure for solutions of Sylvester equations. (English) Zbl 1281.65069 Linear Algebra Appl. 439, No. 4, 856-878 (2013). MSC: 65F30 15A24 65G50 PDFBibTeX XMLCite \textit{S. Miyajima}, Linear Algebra Appl. 439, No. 4, 856--878 (2013; Zbl 1281.65069) Full Text: DOI
Li, Nan; Zhi, Lihong Verified error bounds for isolated singular solutions of polynomial systems: case of breadth one. (English) Zbl 1291.65161 Theor. Comput. Sci. 479, 163-173 (2013). MSC: 65H10 68W30 13P15 65G20 PDFBibTeX XMLCite \textit{N. Li} and \textit{L. Zhi}, Theor. Comput. Sci. 479, 163--173 (2013; Zbl 1291.65161) Full Text: DOI arXiv
Iwane, Hidenao; Yanami, Hitoshi; Anai, Hirokazu; Yokoyama, Kazuhiro An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination. (English) Zbl 1291.68433 Theor. Comput. Sci. 479, 43-69 (2013). MSC: 68W30 03C10 PDFBibTeX XMLCite \textit{H. Iwane} et al., Theor. Comput. Sci. 479, 43--69 (2013; Zbl 1291.68433) Full Text: DOI
Rauh, Andreas; Auer, Ekaterina; Dötschel, Thomas; Aschemann, Harald Verified stability analysis of continuous-time control systems with bounded parameter uncertainties and stochastic disturbances. (English) Zbl 1246.93122 Computing 94, No. 2-4, 345-356 (2012). MSC: 93E15 93C41 93C73 93B52 93C10 PDFBibTeX XMLCite \textit{A. Rauh} et al., Computing 94, No. 2--4, 345--356 (2012; Zbl 1246.93122) Full Text: DOI
Zimmer, Michael; Krämer, Walter; Popova, Evgenija D. Solvers for the verified solution of parametric linear systems. (English) Zbl 1238.65021 Computing 94, No. 2-4, 109-123 (2012). MSC: 65F05 65F50 65G20 65G99 65Y05 65Y20 PDFBibTeX XMLCite \textit{M. Zimmer} et al., Computing 94, No. 2--4, 109--123 (2012; Zbl 1238.65021) Full Text: DOI
Frommer, Andreas; Hashemi, Behnam Verified error bounds for solutions of Sylvester matrix equations. (English) Zbl 1236.65045 Linear Algebra Appl. 436, No. 2, 405-420 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F30 15A24 65F05 65G20 65G30 PDFBibTeX XMLCite \textit{A. Frommer} and \textit{B. Hashemi}, Linear Algebra Appl. 436, No. 2, 405--420 (2012; Zbl 1236.65045) Full Text: DOI
Galias, Zbigniew; Tucker, Warwick Validated study of the existence of short cycles for chaotic systems using symbolic dynamics and interval tools. (English) Zbl 1210.34044 Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 2, 551-563 (2011). MSC: 34C05 37B10 34C28 PDFBibTeX XMLCite \textit{Z. Galias} and \textit{W. Tucker}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 2, 551--563 (2011; Zbl 1210.34044) Full Text: DOI
Chen, Xiaojun; Frommer, Andreas; Lang, Bruno Computational existence proofs for spherical \(t\)-designs. (English) Zbl 1208.65032 Numer. Math. 117, No. 2, 289-305 (2011). MSC: 65D32 41A55 41A63 65H10 65G30 65G20 PDFBibTeX XMLCite \textit{X. Chen} et al., Numer. Math. 117, No. 2, 289--305 (2011; Zbl 1208.65032) Full Text: DOI
Aschemann, H.; Minisini, J.; Rauh, A. Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics. II. (English) Zbl 1268.93061 J. Comput. Syst. Sci. Int. 49, No. 6, 833-846 (2010). MSC: 93B51 65G30 93B35 93C10 93C95 PDFBibTeX XMLCite \textit{H. Aschemann} et al., J. Comput. Syst. Sci. Int. 49, No. 6, 833--846 (2010; Zbl 1268.93061) Full Text: DOI
Rump, Siegfried M.; Graillat, Stef Verified error bounds for multiple roots of systems of nonlinear equations. (English) Zbl 1201.65081 Numer. Algorithms 54, No. 3, 359-377 (2010). Reviewer: Svetoslav Markov (Sofia) MSC: 65H10 65G20 65H04 65F15 PDFBibTeX XMLCite \textit{S. M. Rump} and \textit{S. Graillat}, Numer. Algorithms 54, No. 3, 359--377 (2010; Zbl 1201.65081) Full Text: DOI
Auer, Ekaterina; Luther, Wolfram Uses of new sensitivity and DAE solving methods in SmartMobile for verified analysis of mechanical systems. (English) Zbl 1300.68054 Int. J. Appl. Math. Comput. Sci. 19, No. 3, 455-467 (2009). MSC: 68U20 70-04 93A30 PDFBibTeX XMLCite \textit{E. Auer} and \textit{W. Luther}, Int. J. Appl. Math. Comput. Sci. 19, No. 3, 455--467 (2009; Zbl 1300.68054) Full Text: DOI
Rauh, Andreas; Brill, Michael; Günther, Clemens A novel interval arithmetic approach for solving differential-algebraic equations with ValEncIA-IVP. (English) Zbl 1300.93075 Int. J. Appl. Math. Comput. Sci. 19, No. 3, 381-397 (2009). MSC: 93B40 65G40 93-04 PDFBibTeX XMLCite \textit{A. Rauh} et al., Int. J. Appl. Math. Comput. Sci. 19, No. 3, 381--397 (2009; Zbl 1300.93075) Full Text: DOI
Zalewski, Bart F.; Mullen, Robert L.; Muhanna, Rafi L. Interval boundary element method in the presence of uncertain boundary conditions, integration errors, and truncation errors. (English) Zbl 1244.65213 Eng. Anal. Bound. Elem. 33, No. 4, 508-513 (2009). MSC: 65N38 65G40 PDFBibTeX XMLCite \textit{B. F. Zalewski} et al., Eng. Anal. Bound. Elem. 33, No. 4, 508--513 (2009; Zbl 1244.65213) Full Text: DOI
Zalewski, Bart F.; Mullen, Robert L. Worst case bounds on the point-wise discretization error in boundary element method for the elasticity problem. (English) Zbl 1229.74144 Comput. Methods Appl. Mech. Eng. 198, No. 37-40, 2996-3005 (2009). MSC: 74S15 74B05 65N15 65N38 PDFBibTeX XMLCite \textit{B. F. Zalewski} and \textit{R. L. Mullen}, Comput. Methods Appl. Mech. Eng. 198, No. 37--40, 2996--3005 (2009; Zbl 1229.74144) Full Text: DOI
Zalewski, B. F.; Mullen, R. L. Local discretization error bounds using interval boundary element method. (English) Zbl 1183.74345 Int. J. Numer. Methods Eng. 78, No. 4, 403-428 (2009). MSC: 74S15 PDFBibTeX XMLCite \textit{B. F. Zalewski} and \textit{R. L. Mullen}, Int. J. Numer. Methods Eng. 78, No. 4, 403--428 (2009; Zbl 1183.74345) Full Text: DOI
Kanno, Masaaki; Anai, Hirokazu Computer algebra for guaranteed accuracy. How does it help? (English) Zbl 1191.68889 Japan J. Ind. Appl. Math. 26, No. 2-3, 517-530 (2009). MSC: 68W30 93C99 PDFBibTeX XMLCite \textit{M. Kanno} and \textit{H. Anai}, Japan J. Ind. Appl. Math. 26, No. 2--3, 517--530 (2009; Zbl 1191.68889) Full Text: DOI Euclid
Nakaya, Yusuke; Nishi, Tetsuo; Oishi, Shin’ichi; Claus, Martin Numerical existence proof of five solutions for certain two-transistor circuit equations. (English) Zbl 1191.94155 Japan J. Ind. Appl. Math. 26, No. 2-3, 327-336 (2009). MSC: 94C05 PDFBibTeX XMLCite \textit{Y. Nakaya} et al., Japan J. Ind. Appl. Math. 26, No. 2--3, 327--336 (2009; Zbl 1191.94155) Full Text: DOI Euclid
Alefeld, Goetz Verified numerical computation for nonlinear equations. (English) Zbl 1186.65056 Japan J. Ind. Appl. Math. 26, No. 2-3, 297-315 (2009). Reviewer: Jiří Rohn (Praha) MSC: 65G30 65H05 65G20 PDFBibTeX XMLCite \textit{G. Alefeld}, Japan J. Ind. Appl. Math. 26, No. 2--3, 297--315 (2009; Zbl 1186.65056) Full Text: DOI Euclid
Ogita, Takeshi; Oishi, Shin’ichi Fast verified solutions of linear systems. (English) Zbl 1184.65046 Japan J. Ind. Appl. Math. 26, No. 2-3, 169-190 (2009). MSC: 65F30 65G20 65G30 PDFBibTeX XMLCite \textit{T. Ogita} and \textit{S. Oishi}, Japan J. Ind. Appl. Math. 26, No. 2--3, 169--190 (2009; Zbl 1184.65046) Full Text: DOI Euclid
Okumura, Kohshi Application of the Krawczyk-Moore-Jones algorithm to electric circuit analysis and its further development. (English) Zbl 1191.94157 Japan J. Ind. Appl. Math. 26, No. 2-3, 145-167 (2009). MSC: 94C05 68W10 PDFBibTeX XMLCite \textit{K. Okumura}, Japan J. Ind. Appl. Math. 26, No. 2--3, 145--167 (2009; Zbl 1191.94157) Full Text: DOI Euclid
Lee, Tsung-Lin; Santoprete, Manuele Central configurations of the five-body problem with equal masses. (English) Zbl 1204.70013 Celest. Mech. Dyn. Astron. 104, No. 4, 369-381 (2009). MSC: 70F10 70F15 PDFBibTeX XMLCite \textit{T.-L. Lee} and \textit{M. Santoprete}, Celest. Mech. Dyn. Astron. 104, No. 4, 369--381 (2009; Zbl 1204.70013) Full Text: DOI arXiv
Wilczak, Daniel; Zgliczyński, Piotr Period doubling in the Rössler system – a computer assisted proof. (English) Zbl 1177.37083 Found. Comput. Math. 9, No. 5, 611-649 (2009). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37M20 37N30 PDFBibTeX XMLCite \textit{D. Wilczak} and \textit{P. Zgliczyński}, Found. Comput. Math. 9, No. 5, 611--649 (2009; Zbl 1177.37083) Full Text: DOI arXiv
Yamamura, Kiyotaka; Suda, Koki; Tamura, Naoya LP narrowing: A new strategy for finding all solutions of nonlinear equations. (English) Zbl 1175.65056 Appl. Math. Comput. 215, No. 1, 405-413 (2009). MSC: 65H05 PDFBibTeX XMLCite \textit{K. Yamamura} et al., Appl. Math. Comput. 215, No. 1, 405--413 (2009; Zbl 1175.65056) Full Text: DOI
Wang, Yan; Nnaji, Bartholomew O. Solving interval constraints by linearization in computer-aided design. (English) Zbl 1110.65018 Reliab. Comput. 13, No. 2, 211-244 (2007). MSC: 65D17 65G30 65F10 PDFBibTeX XMLCite \textit{Y. Wang} and \textit{B. O. Nnaji}, Reliab. Comput. 13, No. 2, 211--244 (2007; Zbl 1110.65018) Full Text: DOI
Schwandt, Hartmut Parallel interval Newton-like Schwarz methods for almost linear parabolic problems. (English) Zbl 1110.65092 J. Comput. Appl. Math. 199, No. 2, 437-444 (2007). Reviewer: Srinivasan Natesan (Assam) MSC: 65M55 65M06 65G40 35K55 65H10 65Y05 PDFBibTeX XMLCite \textit{H. Schwandt}, J. Comput. Appl. Math. 199, No. 2, 437--444 (2007; Zbl 1110.65092) Full Text: DOI
Syam, Muhammed I. Nonlinear optimization exclusion tests for finding all solutions of nonlinear equations. (English) Zbl 1087.65554 Appl. Math. Comput. 170, No. 2, 1104-1116 (2005). MSC: 65H05 90C05 65Y20 65G40 PDFBibTeX XMLCite \textit{M. I. Syam}, Appl. Math. Comput. 170, No. 2, 1104--1116 (2005; Zbl 1087.65554) Full Text: DOI
Rump, Siegfried M. Ten methods to bound multiple roots of polynomials. (English) Zbl 1030.65046 J. Comput. Appl. Math. 156, No. 2, 403-432 (2003). Reviewer: Alyson Reeves (Bowie) MSC: 65H05 65G50 65Y20 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{S. M. Rump}, J. Comput. Appl. Math. 156, No. 2, 403--432 (2003; Zbl 1030.65046) Full Text: DOI
Yamamura, Kiyotaka; Fujioka, Tsuyoshi Finding all solutions of nonlinear equations using the dual simplex method. (English) Zbl 1018.65069 J. Comput. Appl. Math. 152, No. 1-2, 587-595 (2003). MSC: 65H10 65G30 90C05 65K05 PDFBibTeX XMLCite \textit{K. Yamamura} and \textit{T. Fujioka}, J. Comput. Appl. Math. 152, No. 1--2, 587--595 (2003; Zbl 1018.65069) Full Text: DOI
Georg, Kurt A new exclusion test. (English) Zbl 1034.65033 J. Comput. Appl. Math. 152, No. 1-2, 147-160 (2003). MSC: 65H10 65Y20 PDFBibTeX XMLCite \textit{K. Georg}, J. Comput. Appl. Math. 152, No. 1--2, 147--160 (2003; Zbl 1034.65033) Full Text: DOI
Bischof, Christian H.; Lang, Bruno; Marquardt, Wolfgang; Mönnigmann, Martin Verified determination of singularities in chemical processes. (English) Zbl 1395.92192 Krämer, Walter (ed.) et al., Scientific computing, validated numerics, interval methods, Karlsruhe, Germany, September 19–22, 2000. New York, NY: Springer (ISBN 978-0-306-46706-6/hbk; 978-1-4757-6484-0/ebook). 305-316 (2001). MSC: 92E20 65K05 90C57 65H10 PDFBibTeX XMLCite \textit{C. H. Bischof} et al., in: Scientific computing, validated numerics, interval methods, Karlsruhe, Germany, September 19--22, 2000. New York, NY: Springer. 305--316 (2001; Zbl 1395.92192) Full Text: DOI
Alefeld, Götz; Mayer, Günter Interval analysis: Theory and applications. (English) Zbl 0995.65056 J. Comput. Appl. Math. 121, No. 1-2, 421-464 (2000). MSC: 65G30 65-02 76F10 65F15 65G40 65G20 65H10 65L05 65N06 65Y15 PDFBibTeX XMLCite \textit{G. Alefeld} and \textit{G. Mayer}, J. Comput. Appl. Math. 121, No. 1--2, 421--464 (2000; Zbl 0995.65056) Full Text: DOI
Yamamura, Kiyotaka; Nishizawa, Masaki Finding all solutions of a class of nonlinear equations using an improved LP test. (English) Zbl 1306.65205 Japan J. Ind. Appl. Math. 16, No. 3, 349-368 (1999). MSC: 65H10 65G20 90C08 PDFBibTeX XMLCite \textit{K. Yamamura} and \textit{M. Nishizawa}, Japan J. Ind. Appl. Math. 16, No. 3, 349--368 (1999; Zbl 1306.65205) Full Text: DOI
Knudsen, Carsten; Stauning, Ole Exact numerical methods in dynamical systems theory. (English) Zbl 0980.37036 Chaos Solitons Fractals 9, No. 8, 1339-1358 (1998). MSC: 37M99 37E15 65H99 65Q05 PDFBibTeX XMLCite \textit{C. Knudsen} and \textit{O. Stauning}, Chaos Solitons Fractals 9, No. 8, 1339--1358 (1998; Zbl 0980.37036) Full Text: DOI
Van Hentenryck, Pascal A gentle introduction to Numerica. (English) Zbl 0910.68095 Artif. Intell. 103, No. 1-2, 209-235 (1998). MSC: 68W30 PDFBibTeX XMLCite \textit{P. Van Hentenryck}, Artif. Intell. 103, No. 1--2, 209--235 (1998; Zbl 0910.68095) Full Text: DOI
Yamamura, Kiyotaka; Kawata, Hitomi; Tokue, Ai Interval solution of nonlinear equations using linear programming. (English) Zbl 0908.65038 BIT 38, No. 1, 186-199 (1998). Reviewer: S.Markov (Sofia) MSC: 65H10 65G30 65K05 90C05 PDFBibTeX XMLCite \textit{K. Yamamura} et al., BIT 38, No. 1, 186--199 (1998; Zbl 0908.65038) Full Text: DOI
Gupta, D. K.; Kaul, C. N. A modification of Krawczyk’s algorithm. (English) Zbl 0905.65062 Int. J. Comput. Math. 66, No. 1-2, 67-77 (1998). Reviewer: G.Mayer (Rostock) MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{D. K. Gupta} and \textit{C. N. Kaul}, Int. J. Comput. Math. 66, No. 1--2, 67--77 (1998; Zbl 0905.65062) Full Text: DOI
Michel, Laurent; Van Hentenryck, Pascal Helios: A modeling language for global optimization and its implementation in Newton. (English) Zbl 0905.65070 Theor. Comput. Sci. 173, No. 1, 3-48 (1997). MSC: 65K05 65G30 90C30 68N17 65Y20 PDFBibTeX XMLCite \textit{L. Michel} and \textit{P. Van Hentenryck}, Theor. Comput. Sci. 173, No. 1, 3--48 (1997; Zbl 0905.65070) Full Text: DOI
Rump, S. M. Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems. (English) Zbl 0862.65033 Computing 57, No. 1, 77-84 (1996). Reviewer: M.Kracht (Düsseldorf) MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{S. M. Rump}, Computing 57, No. 1, 77--84 (1996; Zbl 0862.65033) Full Text: DOI
Rump, Siegfried M. Verified solution of large systems and global optimization problems. (English) Zbl 0866.65035 J. Comput. Appl. Math. 60, No. 1-2, 201-218 (1995). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H10 65K05 90C30 65G30 PDFBibTeX XMLCite \textit{S. M. Rump}, J. Comput. Appl. Math. 60, No. 1--2, 201--218 (1995; Zbl 0866.65035) Full Text: DOI
Heindl, Gerhard Experiences with a method for enclosing solutions of systems of equations. (English) Zbl 0866.65034 J. Comput. Appl. Math. 60, No. 1-2, 63-76 (1995). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{G. Heindl}, J. Comput. Appl. Math. 60, No. 1--2, 63--76 (1995; Zbl 0866.65034) Full Text: DOI
Frommer, Andreas; Schwandt, Hartmut Asynchronous parallel methods for enclosing solutions of nonlinear equations. (English) Zbl 0837.65051 J. Comput. Appl. Math. 60, No. 1-2, 47-62 (1995). Reviewer: I.N.Molchanov (Kiev) MSC: 65H10 65Y05 65G30 65N06 35J65 PDFBibTeX XMLCite \textit{A. Frommer} and \textit{H. Schwandt}, J. Comput. Appl. Math. 60, No. 1--2, 47--62 (1995; Zbl 0837.65051) Full Text: DOI
Eriksson, Jerry; Lindström, Per A parallel interval method implementation for global optimization using dynamic load balancing. (English) Zbl 0833.65053 Reliab. Comput. 1, No. 1, 77-91 (1995). Reviewer: H.Ratschek (Düsseldorf) MSC: 65K05 65Y05 65G30 90C57 90C30 PDFBibTeX XMLCite \textit{J. Eriksson} and \textit{P. Lindström}, Reliab. Comput. 1, No. 1, 77--91 (1995; Zbl 0833.65053) Full Text: DOI
Hong, H.; Stahl, V. Safe starting regions by fixed points and tightening. (English) Zbl 0819.65088 Computing 53, No. 3-4, 323-335 (1994). Reviewer: A.Frommer (Wuppertal) MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{H. Hong} and \textit{V. Stahl}, Computing 53, No. 3--4, 323--335 (1994; Zbl 0819.65088) Full Text: DOI
Hansen, E. R.; Walster, G. W. Nonlinear equations and optimization. (English) Zbl 0770.65037 Comput. Math. Appl. 25, No. 10-11, 125-145 (1993). MSC: 65H10 65K05 65G30 PDFBibTeX XMLCite \textit{E. R. Hansen} and \textit{G. W. Walster}, Comput. Math. Appl. 25, No. 10--11, 125--145 (1993; Zbl 0770.65037) Full Text: DOI
Rump, S. M. On the solution of interval linear systems. (English) Zbl 0753.65030 Computing 47, No. 3-4, 337-353 (1992). Reviewer: H.Fischer (München) MSC: 65F10 65G30 PDFBibTeX XMLCite \textit{S. M. Rump}, Computing 47, No. 3--4, 337--353 (1992; Zbl 0753.65030) Full Text: DOI
Jansson, C. Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side. (English) Zbl 0729.65016 Computing 46, No. 3, 265-274 (1991). Reviewer: H.Ratschek (Düsseldorf) MSC: 65F05 65G30 PDFBibTeX XMLCite \textit{C. Jansson}, Computing 46, No. 3, 265--274 (1991; Zbl 0729.65016) Full Text: DOI
Ratschek, H.; Voller, R. L. What can interval analysis do for global optimization? (English) Zbl 0752.65054 J. Glob. Optim. 1, No. 2, 111-130 (1991). Reviewer: G.Mayer (Karlsruhe) MSC: 65K05 65G30 65-02 90C30 PDFBibTeX XMLCite \textit{H. Ratschek} and \textit{R. L. Voller}, J. Glob. Optim. 1, No. 2, 111--130 (1991; Zbl 0752.65054) Full Text: DOI
Jansson, C. A geometric approach for computing a posteriori error bounds for the solution of a linear system. (English) Zbl 0738.65040 Computing 47, No. 1, 1-9 (1991). Reviewer: W.Govaerts (Gent) MSC: 65F30 PDFBibTeX XMLCite \textit{C. Jansson}, Computing 47, No. 1, 1--9 (1991; Zbl 0738.65040) Full Text: DOI
Rump, S. M. Estimation of the sensitivity of linear and nonlinear algebraic problems. (English) Zbl 0736.65036 Linear Algebra Appl. 153, 1-34 (1991). Reviewer: N.F.F.Ebecken (Rio de Janeiro) MSC: 65H10 65F05 65G50 PDFBibTeX XMLCite \textit{S. M. Rump}, Linear Algebra Appl. 153, 1--34 (1991; Zbl 0736.65036) Full Text: DOI
Rump, Siegfried M. Rigorous sensitivity analysis for systems of linear and nonlinear equations. (English) Zbl 0701.65039 Math. Comput. 54, No. 190, 721-736 (1990). Reviewer: H.Ratschek MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{S. M. Rump}, Math. Comput. 54, No. 190, 721--736 (1990; Zbl 0701.65039) Full Text: DOI
Rump, S. M. Guaranteed inclusions for the complex generalized eigenproblem. (English) Zbl 0676.65028 Computing 42, No. 2-3, 225-238 (1989). Reviewer: A.Ruhe MSC: 65F15 65G30 15A42 PDFBibTeX XMLCite \textit{S. M. Rump}, Computing 42, No. 2--3, 225--238 (1989; Zbl 0676.65028) Full Text: DOI
Shen, Zuhe A class of componentwise Krawczyk-Moore type iteration methods. (English) Zbl 0672.65029 Computing 41, No. 1-2, 149-152 (1989). Reviewer: Yu.Shokin MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{Z. Shen}, Computing 41, No. 1--2, 149--152 (1989; Zbl 0672.65029) Full Text: DOI
Krawczyk, R. Conditionally isotone interval operators. (English) Zbl 0627.65053 Computing 39, 261-270 (1987). MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{R. Krawczyk}, Computing 39, 261--270 (1987; Zbl 0627.65053) Full Text: DOI
Rall, L. B. Interval methods for fixed-point problems. (English) Zbl 0586.65046 Numer. Funct. Anal. Optimization 9, 35-59 (1987). MSC: 65J15 65G30 65R20 47H07 45G10 47J25 PDFBibTeX XMLCite \textit{L. B. Rall}, Numer. Funct. Anal. Optim. 9, 35--59 (1987; Zbl 0586.65046) Full Text: DOI
Krawczyk, Rudolf Centered forms and interval operators. (English) Zbl 0555.65029 Computing 34, 243-259 (1985). MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{R. Krawczyk}, Computing 34, 243--259 (1985; Zbl 0555.65029) Full Text: DOI
Demmel, J. W.; Krückeberg, F. An interval algorithm for solving systems of linear equations to prespecified accuracy. (English) Zbl 0555.65019 Computing 34, 117-129 (1985). MSC: 65F05 65G30 PDFBibTeX XMLCite \textit{J. W. Demmel} and \textit{F. Krückeberg}, Computing 34, 117--129 (1985; Zbl 0555.65019) Full Text: DOI
Neumaier, Arnold New techniques for the analysis of linear interval equations. (English) Zbl 0558.65019 Linear Algebra Appl. 58, 273-325 (1984). Reviewer: G.Alefeld MSC: 65F05 65F10 65G30 PDFBibTeX XMLCite \textit{A. Neumaier}, Linear Algebra Appl. 58, 273--325 (1984; Zbl 0558.65019) Full Text: DOI
Schmidt, Jochen W.; Schneider, Harald Enclosing methods in perturbed nonlinear operator equations. (English) Zbl 0518.65039 Computing 32, 1-11 (1984). MSC: 65J15 47H07 PDFBibTeX XMLCite \textit{J. W. Schmidt} and \textit{H. Schneider}, Computing 32, 1--11 (1984; Zbl 0518.65039) Full Text: DOI
Krawczyk, R. Interval iterations for including a set of solutions. (English) Zbl 0518.65023 Computing 32, 13-31 (1984). MSC: 65G30 65H10 PDFBibTeX XMLCite \textit{R. Krawczyk}, Computing 32, 13--31 (1984; Zbl 0518.65023) Full Text: DOI
Hansen, E. R.; Greenberg, R. I. An interval Newton method. (English) Zbl 0526.65040 Appl. Math. Comput. 12, 89-98 (1983). MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{E. R. Hansen} and \textit{R. I. Greenberg}, Appl. Math. Comput. 12, 89--98 (1983; Zbl 0526.65040) Full Text: DOI
Shen, Zuhe On some classical existence theorems. (English) Zbl 0523.65029 Nonlinear Anal., Theory Methods Appl. 7, 1029-1033 (1983). MSC: 65G30 65J05 PDFBibTeX XMLCite \textit{Z. Shen}, Nonlinear Anal., Theory Methods Appl. 7, 1029--1033 (1983; Zbl 0523.65029) Full Text: DOI
Krawczyk, R. Interval operators of a function of which the Lipschitz matrix is an interval M-matrix. (English) Zbl 0506.65018 Computing 31, 245-253 (1983). MSC: 65H10 65G30 PDFBibTeX XMLCite \textit{R. Krawczyk}, Computing 31, 245--253 (1983; Zbl 0506.65018) Full Text: DOI
Moore, R. E.; Shen, Zuhe An interval version of Chebyshev’s method for nonlinear operator equations. (English) Zbl 0505.65015 Nonlinear Anal., Theory Methods Appl. 7, 21-34 (1983). MSC: 65J15 65G30 65L05 65L10 65N22 PDFBibTeX XMLCite \textit{R. E. Moore} and \textit{Z. Shen}, Nonlinear Anal., Theory Methods Appl. 7, 21--34 (1983; Zbl 0505.65015) Full Text: DOI