Edit Profile (opens in new tab) Trench, William F. Co-Author Distance Author ID: trench.william-f Published as: Trench, William F.; Trench, W. F.; Trench, Willian F. more...less Documents Indexed: 129 Publications since 1959, including 3 Books Co-Authors: 7 Co-Authors with 12 Joint Publications 105 Co-Co-Authors all top 5 Co-Authors 116 single-authored 5 Kusano, Takaŝi 2 Kolman, Bernard 1 Bahar, Leon Y. 1 Greville, Thomas Nall Eden 1 Harris, Bennette R. 1 Norman, Edward 1 Scheinok, P. A. 1 Tabachnikov, Serge L. all top 5 Serials 27 Linear Algebra and its Applications 15 Proceedings of the American Mathematical Society 7 Journal of Mathematical Analysis and Applications 6 SIAM Journal on Matrix Analysis and Applications 6 SIAM Journal on Mathematical Analysis 4 American Mathematical Monthly 4 Computers & Mathematics with Applications 4 Hiroshima Mathematical Journal 4 Journal of Computational and Applied Mathematics 4 Journal of the Society for Industrial & Applied Mathematics 3 Linear and Multilinear Algebra 3 Journal of Differential Equations 3 Transactions of the American Mathematical Society 2 Funkcialaj Ekvacioj. Serio Internacia 2 SIAM Journal on Algebraic and Discrete Methods 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Scientific Computing 2 Numerical Linear Algebra with Applications 2 Journal of Difference Equations and Applications 1 Houston Journal of Mathematics 1 International Journal of Non-Linear Mechanics 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Czechoslovak Mathematical Journal 1 Journal of the London Mathematical Society. Second Series 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 SIAM Journal on Numerical Analysis 1 Differential and Integral Equations 1 Panamerican Mathematical Journal 1 Dynamic Systems and Applications 1 SIAM Review 1 Cubo 1 Bulletin of the American Mathematical Society 1 Annals of Mathematical Statistics 1 Special Matrices all top 5 Fields 43 Linear and multilinear algebra; matrix theory (15-XX) 42 Ordinary differential equations (34-XX) 18 Numerical analysis (65-XX) 15 Difference and functional equations (39-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 5 Statistics (62-XX) 4 Sequences, series, summability (40-XX) 3 Real functions (26-XX) 3 Approximations and expansions (41-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Probability theory and stochastic processes (60-XX) 1 Partial differential equations (35-XX) 1 Operator theory (47-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 103 Publications have been cited 988 times in 695 Documents Cited by ▼ Year ▼ An algorithm for the inversion of finite Toeplitz matrices. Zbl 0131.36002 Trench, William F. 158 1964 Canonical forms and principal systems for general disconjugate equations. Zbl 0289.34051 Trench, William F. 79 1974 Characterization and properties of matrices with generalized symmetry or skew symmetry. Zbl 1046.15028 Trench, William F. 44 2004 Inverse eigenproblems and associated approximation problems for matrices with generalized symmetry or skew symmetry. Zbl 1087.15013 Trench, William F. 38 2004 Minimization problems for \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices. Zbl 1059.15019 Trench, William F. 34 2004 On the eigenvalue problem for Toeplitz band matrices. Zbl 0568.15005 Trench, William F. 32 1985 On the asymptotic behaviour of solutions of second order linear differential equations. Zbl 0116.29304 Trench, William F. 31 1963 An algorithm for the inversion of finite Hankel matrices. Zbl 0135.17801 Trench, William F. 23 1965 Numerical solution of the eigenvalue problem for Hermitian Toeplitz matrices. Zbl 0676.65027 Trench, William F. 21 1989 Existence of global solutions with prescribed asymptotic behavior for nonlinear ordinary differential equations. Zbl 0593.34039 Kusano, Takaŝi; Trench, William F. 20 1985 Characterization and properties of \((R,S)\)-symmetric, \((R,S)\)-skew symmetric, and \((R,S)\)-conjugate matrices. Zbl 1080.15022 Trench, William F. 20 2005 Introduction to real analysis. Zbl 1204.00023 Trench, William F. 20 2003 Hermitian, Hermitian \(R\)-symmetric, and Hermitian \(R\)-skew symmetric Procrustes problems. Zbl 1121.15016 Trench, William F. 19 2004 Numerical solution of the inverse eigenvalue problem for real symmetric Toeplitz matrices. Zbl 0888.65045 Trench, William F. 18 1997 Weighting coefficients for the prediction of stationary time series from the finite past. Zbl 0275.60055 Trench, William F. 17 1967 Global existence theorems for solutions of nonlinear differential equations with prescribed asymptotic behaviour. Zbl 0578.34045 Kusano, Takaŝi; Trench, William F. 16 1985 Characterization and properties of matrices with \(k\)-involutory symmetries. Zbl 1167.15020 Trench, William F. 15 2008 Band matrices with Toeplitz inverses. Zbl 0428.15002 Greville, T. N. E.; Trench, William F. 13 1979 Invertibly convergent infinite products of matrices, with applications to difference equations. Zbl 0846.40002 Trench, W. F. 13 1995 Spectral evolution of a one-parameter extension of a real symmetric Toeplitz matrix. Zbl 0717.15008 Trench, William F. 13 1990 Inversion of Toeplitz band matrices. Zbl 0293.65014 Trench, William F. 12 1974 Oscillation properties of perturbed disconjugate equations. Zbl 0321.34027 Trench, William F. 12 1975 Linear perturbations of a nonoscillatory second order equation. Zbl 0594.34057 Trench, William F. 12 1986 Characterization and properties of matrices with \(k\)-involutory symmetries. II. Zbl 1205.15014 Trench, William F. 12 2010 Asymptotic behavior of solutions of Poincaré recurrence systems. Zbl 0805.39001 Trench, W. F. 11 1994 Asymptotic distribution of the spectra of a class of generalized Kac-Murdock-Szegö matrices. Zbl 0942.15006 Trench, William F. 11 1999 Properties of unilevel block circulants. Zbl 1217.15039 Trench, William F. 11 2009 Explicit inversion formulas for Toeplitz band matrices. Zbl 0573.15002 Trench, William F. 10 1985 Interlacement of the even and odd spectra of real symmetric Toeplitz matrices. Zbl 0790.15019 Trench, William F. 9 1993 Invertibly convergent infinite products of matrices. Zbl 0953.40003 Trench, William F. 8 1999 Extensions of a theorem of Wintner on systems with asymptotically constant solutions. Zbl 0597.34007 Trench, William F. 8 1986 Asymptotic behavior of solutions of Poincaré difference equations. Zbl 0783.39002 Trench, William F. 7 1993 Asymptotic behavior of solutions of Emden-Fowler difference equations with oscillating coefficients. Zbl 0796.39001 Trench, William F. 7 1993 Numerical solution of the eigenvalue problem for symmetric rationally generated Toeplitz matrices. Zbl 0647.65023 Trench, William F. 7 1988 Spectral distribution of generalized Kac-Murdock-Szegö matrices. Zbl 1071.15011 Trench, William F. 7 2002 Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems. Zbl 0935.39004 Trench, W. F. 7 1998 Linear perturbations of a nonoscillatory second order difference equation. Zbl 0984.39005 Trench, William F. 7 2001 Properties of multilevel block \(\alpha \)-circulants. Zbl 1178.15017 Trench, William F. 6 2009 On the eigenvalue problem for Toeplitz matrices generated by rational functions. Zbl 0569.15004 Trench, William F. 6 1985 Systems of differential equations subject to mild integral conditions. Zbl 0514.34031 Trench, William F. 6 1983 Asymptotic behavior of solutions of a linear second-order difference equation. Zbl 0758.39004 Trench, William F. 6 1992 Some spectral properties of Hermitian Toeplitz matrices. Zbl 0813.15004 Trench, William F. 5 1994 Asymptotic distribution of the even and odd spectra of real symmetric Toeplitz matrices. Zbl 0947.15009 Trench, William F. 5 1999 A sufficient condition for eventual disconjugacy. Zbl 0321.34026 Trench, William F. 5 1975 Solution of systems with Toeplitz matrices generated by rational functions. Zbl 0588.15003 Trench, William F. 5 1986 On an explicit method for the solution of a Stefan problem. Zbl 0088.34103 Trench, William F. 5 1959 On the stability of midpoint smoothing with Legendre polynomials. Zbl 0234.65016 Trench, William F. 5 1967 Asymptotic behavior of solutions of \(Lu = g(t,u,\dots ,u^{(k-1)})\). Zbl 0235.34083 Trench, William F. 5 1972 Eventual disconjugacy of a linear differential equation. Zbl 0529.34041 Trench, William F. 5 1983 A note on a Toeplitz inversion formula. Zbl 0711.15030 Trench, William F. 5 1990 Linear perturbations of a nonoscillatory second order differential equation II. Zbl 1032.34049 Trench, William F. 4 2003 Nonnegative and alternating expansions of one set of orthogonal polynomials in terms of another. Zbl 0223.42018 Trench, William F. 4 1973 Conditional convergence of infinite products. Zbl 0979.40001 Trench, William F. 4 1999 Proof of a conjecture of Askey on orthogonal expansions with positive coefficients. Zbl 0314.42013 Trench, William F. 4 1975 Absolute equal distribution of families of finite sets. Zbl 1037.15011 Trench, William F. 4 2003 Functional perturbations of second order differential equations. Zbl 0577.34060 Trench, William F. 4 1985 Asymptotics of differential systems with deviating arguments. Zbl 0581.34056 Trench, William F. 4 1984 An elementary view of Weyl’s theory of equal distribution. Zbl 1275.11105 Trench, William F. 4 2012 Characteristic polynomials of symmetric rationally generated Toeplitz matrices. Zbl 0651.15009 Trench, William F. 3 1987 Numerical solution of the eigenvalue problem for symmetric rationally generated Toeplitz matrices. Zbl 0669.65029 Trench, W. F. 3 1988 On the extrapolation of a special class of stationary time series. Zbl 0202.49202 Trench, William F. 3 1965 Properties of some generalizations of Kac-Murdock-Szegö matrices. Zbl 0994.15007 Trench, William F. 3 2001 Systems of difference equations with asymptotically constant solutions. Zbl 0959.39003 Trench, William F. 3 2000 Multivariable calculus with linear algebra and series. Zbl 0272.00002 Trench, William F.; Kolman, Bernard 3 1972 Absolute equal distribution of the spectra of Hermitian matrices. Zbl 1030.15008 Trench, William F. 3 2003 Global existence of nonoscillatory solutions of perturbed general disconjugate equations. Zbl 0638.34028 Kusano, Takaŝi; Trench, William F. 3 1987 On periodicities of certain sequences of residues. Zbl 0101.03104 Trench, William F. 3 1960 Bounds on the generating functions of certain smoothing operations. Zbl 0234.65017 Trench, William F. 3 1967 On nonautonomous linear systems of differential and difference equations with \(R\)-symmetric coefficient matrices. Zbl 1179.34053 Trench, William F. 3 2009 Asymptotic integration of linear differential equations subject to mild integral conditions. Zbl 0567.34008 Trench, William F. 3 1984 Asymptotic behavior of solutions of an \(n\)th order differential equation. Zbl 0542.34051 Trench, William F. 3 1984 Asymptotic theory of perturbed general disconjugate equations. Zbl 0487.34031 Trench, William F. 3 1982 Characterization and properties of \((R,S_\sigma)\)-commutative matrices. Zbl 1246.15021 Trench, William F. 2 2012 A note on computing eigenvalues of banded Hermitian Toeplitz matrices. Zbl 0771.65018 Trench, William F. 2 1993 Continuous smoothing with polynomial weighting. Zbl 0211.51601 Trench, William F. 2 1970 Linear asymptotic equilibrium of nilpotent systems of linear difference equations. Zbl 0942.39008 Trench, William F. 2 1999 Asymptotic integration of linear differential equations subject to integral smallness conditions involving ordinary convergence. Zbl 0328.34049 Trench, William F. 2 1976 Multilevel matrices with involutory symmetries and skew symmetries. Zbl 1082.15042 Trench, William F. 2 2005 Existence and nonoscillation theorems for an Emden-Fowler equation with deviating argument. Zbl 0602.34043 Trench, William F. 2 1986 Global existence of solutions of mixed sublinear-superlinear differential equations. Zbl 0622.34031 Kusano, Takaŝi; Trench, Willian F. 2 1986 On the inversion of a Hilbert type matrix. Zbl 0136.11802 Trench, William F.; Scheinok, P. A. 2 1966 Stability of certain differential equations with homogeneous right hand sides. Zbl 0193.05502 Norman, E.; Trench, William F. 2 1969 Asymptotic theory of perturbed general disconjugate equations. II. Zbl 0563.34036 Trench, William F. 2 1984 Numerical solution of the eigenvalue problem for efficiently structured Hermitian matrices. Zbl 0733.65020 Trench, William F. 2 1991 Asymptotic integration of \(y^{(n)}+P(t)y^\nu=f(t)\) under mild integral smallness conditions. Zbl 0529.34042 Trench, William F. 2 1983 Linear perturbations of a nonoscillatory second order difference equation. II. Zbl 1021.39005 Trench, William F. 1 2002 Discrete minimum variance smoothing of a polynomial plus random noise. Zbl 0223.62107 Trench, William F. 1 1971 Trench’s canonical form for a disconjugate \(n\)th-order linear difference equation. Zbl 0958.39004 Harris, Bennette; Krueger, Robert; Trench, William F. 1 1998 Asymptotic behavior of solutions of perturbed disconjugate equations. Zbl 0238.34054 Trench, William F. 1 1972 Strong discrete minimum variance estimation of a polynomial plus random noise. Zbl 0248.62044 Trench, William F. 1 1973 Orthogonal polynomial expansions with nonnegative coefficients. Zbl 0341.42015 Trench, William F. 1 1976 A note on asymptotic zero distribution of orthogonal polynomials. Zbl 1051.33007 Trench, William F. 1 2003 Global solutions of nonlinear perturbations of linear differential equations. Zbl 0832.34034 Trench, William F. 1 1992 On the eigenvalue problem for a class of band matrices including those with Toeplitz inverses. Zbl 0606.15003 Trench, William F. 1 1986 Eventual disconjugacy of a linear differential equation. II. Zbl 0623.34040 Trench, William F. 1 1985 Linear perturbations of a constant coefficient differential equation subject to mild integral smallness conditions. Zbl 0623.34059 Trench, William F. 1 1986 An elementary note on asymptotic properties of Toeplitz and multilevel Toeplitz matrices. Zbl 1051.15018 Trench, William F. 1 2004 Asymptotic preconditioning of linear homogeneous systems of differential equations. Zbl 1225.34017 Trench, William F. 1 2011 Systems of functional differential equations with asymptotically constant solutions. Zbl 0692.34071 Trench, William F.; Kusano, Takaŝi 1 1988 Efficient application of the Schauder-Tychonoff theorem to systems of functional differential equations. Zbl 0715.34127 Trench, William F. 1 1990 Inverse problems for unilevel block \(\alpha \)-circulants. Zbl 1289.15034 Trench, W. 1 2013 An elementary view of Weyl’s theory of equal distribution. Zbl 1275.11105 Trench, William F. 4 2012 Characterization and properties of \((R,S_\sigma)\)-commutative matrices. Zbl 1246.15021 Trench, William F. 2 2012 Asymptotic preconditioning of linear homogeneous systems of differential equations. Zbl 1225.34017 Trench, William F. 1 2011 Characterization and properties of matrices with \(k\)-involutory symmetries. II. Zbl 1205.15014 Trench, William F. 12 2010 Properties of unilevel block circulants. Zbl 1217.15039 Trench, William F. 11 2009 Properties of multilevel block \(\alpha \)-circulants. Zbl 1178.15017 Trench, William F. 6 2009 On nonautonomous linear systems of differential and difference equations with \(R\)-symmetric coefficient matrices. Zbl 1179.34053 Trench, William F. 3 2009 Characterization and properties of matrices with \(k\)-involutory symmetries. Zbl 1167.15020 Trench, William F. 15 2008 Characterization and properties of \((R,S)\)-symmetric, \((R,S)\)-skew symmetric, and \((R,S)\)-conjugate matrices. Zbl 1080.15022 Trench, William F. 20 2005 Multilevel matrices with involutory symmetries and skew symmetries. Zbl 1082.15042 Trench, William F. 2 2005 Characterization and properties of matrices with generalized symmetry or skew symmetry. Zbl 1046.15028 Trench, William F. 44 2004 Inverse eigenproblems and associated approximation problems for matrices with generalized symmetry or skew symmetry. Zbl 1087.15013 Trench, William F. 38 2004 Minimization problems for \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices. Zbl 1059.15019 Trench, William F. 34 2004 Hermitian, Hermitian \(R\)-symmetric, and Hermitian \(R\)-skew symmetric Procrustes problems. Zbl 1121.15016 Trench, William F. 19 2004 An elementary note on asymptotic properties of Toeplitz and multilevel Toeplitz matrices. Zbl 1051.15018 Trench, William F. 1 2004 Introduction to real analysis. Zbl 1204.00023 Trench, William F. 20 2003 Linear perturbations of a nonoscillatory second order differential equation II. Zbl 1032.34049 Trench, William F. 4 2003 Absolute equal distribution of families of finite sets. Zbl 1037.15011 Trench, William F. 4 2003 Absolute equal distribution of the spectra of Hermitian matrices. Zbl 1030.15008 Trench, William F. 3 2003 A note on asymptotic zero distribution of orthogonal polynomials. Zbl 1051.33007 Trench, William F. 1 2003 Spectral distribution of generalized Kac-Murdock-Szegö matrices. Zbl 1071.15011 Trench, William F. 7 2002 Linear perturbations of a nonoscillatory second order difference equation. II. Zbl 1021.39005 Trench, William F. 1 2002 Linear perturbations of a nonoscillatory second order difference equation. Zbl 0984.39005 Trench, William F. 7 2001 Properties of some generalizations of Kac-Murdock-Szegö matrices. Zbl 0994.15007 Trench, William F. 3 2001 Systems of difference equations with asymptotically constant solutions. Zbl 0959.39003 Trench, William F. 3 2000 Asymptotic distribution of the spectra of a class of generalized Kac-Murdock-Szegö matrices. Zbl 0942.15006 Trench, William F. 11 1999 Invertibly convergent infinite products of matrices. Zbl 0953.40003 Trench, William F. 8 1999 Asymptotic distribution of the even and odd spectra of real symmetric Toeplitz matrices. Zbl 0947.15009 Trench, William F. 5 1999 Conditional convergence of infinite products. Zbl 0979.40001 Trench, William F. 4 1999 Linear asymptotic equilibrium of nilpotent systems of linear difference equations. Zbl 0942.39008 Trench, William F. 2 1999 Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems. Zbl 0935.39004 Trench, W. F. 7 1998 Trench’s canonical form for a disconjugate \(n\)th-order linear difference equation. Zbl 0958.39004 Harris, Bennette; Krueger, Robert; Trench, William F. 1 1998 Numerical solution of the inverse eigenvalue problem for real symmetric Toeplitz matrices. Zbl 0888.65045 Trench, William F. 18 1997 Invertibly convergent infinite products of matrices, with applications to difference equations. Zbl 0846.40002 Trench, W. F. 13 1995 Asymptotic behavior of solutions of Poincaré recurrence systems. Zbl 0805.39001 Trench, W. F. 11 1994 Some spectral properties of Hermitian Toeplitz matrices. Zbl 0813.15004 Trench, William F. 5 1994 Interlacement of the even and odd spectra of real symmetric Toeplitz matrices. Zbl 0790.15019 Trench, William F. 9 1993 Asymptotic behavior of solutions of Poincaré difference equations. Zbl 0783.39002 Trench, William F. 7 1993 Asymptotic behavior of solutions of Emden-Fowler difference equations with oscillating coefficients. Zbl 0796.39001 Trench, William F. 7 1993 A note on computing eigenvalues of banded Hermitian Toeplitz matrices. Zbl 0771.65018 Trench, William F. 2 1993 Asymptotic behavior of solutions of a linear second-order difference equation. Zbl 0758.39004 Trench, William F. 6 1992 Global solutions of nonlinear perturbations of linear differential equations. Zbl 0832.34034 Trench, William F. 1 1992 Mild integrability conditions for global solutions of an elliptic equation. Zbl 0772.35023 Trench, William F. 1 1992 Numerical solution of the eigenvalue problem for efficiently structured Hermitian matrices. Zbl 0733.65020 Trench, William F. 2 1991 Spectral evolution of a one-parameter extension of a real symmetric Toeplitz matrix. Zbl 0717.15008 Trench, William F. 13 1990 A note on a Toeplitz inversion formula. Zbl 0711.15030 Trench, William F. 5 1990 Efficient application of the Schauder-Tychonoff theorem to systems of functional differential equations. Zbl 0715.34127 Trench, William F. 1 1990 Numerical solution of the eigenvalue problem for Hermitian Toeplitz matrices. Zbl 0676.65027 Trench, William F. 21 1989 Numerical solution of the eigenvalue problem for symmetric rationally generated Toeplitz matrices. Zbl 0647.65023 Trench, William F. 7 1988 Numerical solution of the eigenvalue problem for symmetric rationally generated Toeplitz matrices. Zbl 0669.65029 Trench, W. F. 3 1988 Systems of functional differential equations with asymptotically constant solutions. Zbl 0692.34071 Trench, William F.; Kusano, Takaŝi 1 1988 Characteristic polynomials of symmetric rationally generated Toeplitz matrices. Zbl 0651.15009 Trench, William F. 3 1987 Global existence of nonoscillatory solutions of perturbed general disconjugate equations. Zbl 0638.34028 Kusano, Takaŝi; Trench, William F. 3 1987 Linear perturbations of a nonoscillatory second order equation. Zbl 0594.34057 Trench, William F. 12 1986 Extensions of a theorem of Wintner on systems with asymptotically constant solutions. Zbl 0597.34007 Trench, William F. 8 1986 Solution of systems with Toeplitz matrices generated by rational functions. Zbl 0588.15003 Trench, William F. 5 1986 Existence and nonoscillation theorems for an Emden-Fowler equation with deviating argument. Zbl 0602.34043 Trench, William F. 2 1986 Global existence of solutions of mixed sublinear-superlinear differential equations. Zbl 0622.34031 Kusano, Takaŝi; Trench, Willian F. 2 1986 On the eigenvalue problem for a class of band matrices including those with Toeplitz inverses. Zbl 0606.15003 Trench, William F. 1 1986 Linear perturbations of a constant coefficient differential equation subject to mild integral smallness conditions. Zbl 0623.34059 Trench, William F. 1 1986 On the eigenvalue problem for Toeplitz band matrices. Zbl 0568.15005 Trench, William F. 32 1985 Existence of global solutions with prescribed asymptotic behavior for nonlinear ordinary differential equations. Zbl 0593.34039 Kusano, Takaŝi; Trench, William F. 20 1985 Global existence theorems for solutions of nonlinear differential equations with prescribed asymptotic behaviour. Zbl 0578.34045 Kusano, Takaŝi; Trench, William F. 16 1985 Explicit inversion formulas for Toeplitz band matrices. Zbl 0573.15002 Trench, William F. 10 1985 On the eigenvalue problem for Toeplitz matrices generated by rational functions. Zbl 0569.15004 Trench, William F. 6 1985 Functional perturbations of second order differential equations. Zbl 0577.34060 Trench, William F. 4 1985 Eventual disconjugacy of a linear differential equation. II. Zbl 0623.34040 Trench, William F. 1 1985 Asymptotics of differential systems with deviating arguments. Zbl 0581.34056 Trench, William F. 4 1984 Asymptotic integration of linear differential equations subject to mild integral conditions. Zbl 0567.34008 Trench, William F. 3 1984 Asymptotic behavior of solutions of an \(n\)th order differential equation. Zbl 0542.34051 Trench, William F. 3 1984 Asymptotic theory of perturbed general disconjugate equations. II. Zbl 0563.34036 Trench, William F. 2 1984 Systems of differential equations subject to mild integral conditions. Zbl 0514.34031 Trench, William F. 6 1983 Eventual disconjugacy of a linear differential equation. Zbl 0529.34041 Trench, William F. 5 1983 Asymptotic integration of \(y^{(n)}+P(t)y^\nu=f(t)\) under mild integral smallness conditions. Zbl 0529.34042 Trench, William F. 2 1983 Asymptotic theory of perturbed general disconjugate equations. Zbl 0487.34031 Trench, William F. 3 1982 An oscillation condition for differential equations of arbitrary order. Zbl 0481.34023 Trench, William F. 1 1981 Band matrices with Toeplitz inverses. Zbl 0428.15002 Greville, T. N. E.; Trench, William F. 13 1979 Asymptotic integration of linear differential equations subject to integral smallness conditions involving ordinary convergence. Zbl 0328.34049 Trench, William F. 2 1976 Orthogonal polynomial expansions with nonnegative coefficients. Zbl 0341.42015 Trench, William F. 1 1976 Oscillation properties of perturbed disconjugate equations. Zbl 0321.34027 Trench, William F. 12 1975 A sufficient condition for eventual disconjugacy. Zbl 0321.34026 Trench, William F. 5 1975 Proof of a conjecture of Askey on orthogonal expansions with positive coefficients. Zbl 0314.42013 Trench, William F. 4 1975 Canonical forms and principal systems for general disconjugate equations. Zbl 0289.34051 Trench, William F. 79 1974 Inversion of Toeplitz band matrices. Zbl 0293.65014 Trench, William F. 12 1974 Nonnegative and alternating expansions of one set of orthogonal polynomials in terms of another. Zbl 0223.42018 Trench, William F. 4 1973 Strong discrete minimum variance estimation of a polynomial plus random noise. Zbl 0248.62044 Trench, William F. 1 1973 Asymptotic behavior of solutions of \(Lu = g(t,u,\dots ,u^{(k-1)})\). Zbl 0235.34083 Trench, William F. 5 1972 Multivariable calculus with linear algebra and series. Zbl 0272.00002 Trench, William F.; Kolman, Bernard 3 1972 Asymptotic behavior of solutions of perturbed disconjugate equations. Zbl 0238.34054 Trench, William F. 1 1972 Discrete minimum variance smoothing of a polynomial plus random noise. Zbl 0223.62107 Trench, William F. 1 1971 Continuous smoothing with polynomial weighting. Zbl 0211.51601 Trench, William F. 2 1970 Stability of certain differential equations with homogeneous right hand sides. Zbl 0193.05502 Norman, E.; Trench, William F. 2 1969 Weighting coefficients for the prediction of stationary time series from the finite past. Zbl 0275.60055 Trench, William F. 17 1967 On the stability of midpoint smoothing with Legendre polynomials. Zbl 0234.65016 Trench, William F. 5 1967 Bounds on the generating functions of certain smoothing operations. Zbl 0234.65017 Trench, William F. 3 1967 On the inversion of a Hilbert type matrix. Zbl 0136.11802 Trench, William F.; Scheinok, P. A. 2 1966 An algorithm for the inversion of finite Hankel matrices. Zbl 0135.17801 Trench, William F. 23 1965 On the extrapolation of a special class of stationary time series. Zbl 0202.49202 Trench, William F. 3 1965 An algorithm for the inversion of finite Toeplitz matrices. Zbl 0131.36002 Trench, William F. 158 1964 ...and 3 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 776 Authors 57 Trench, William F. 20 Džurina, Jozef 11 Ma, Changfeng 10 Böttcher, Albrecht 10 Grace, Said Rezk 10 Kusano, Takaŝi 9 Thandapani, Ethiraju 9 Wang, Qingwen 8 Grudsky, Sergei Mikhailovich 8 Hu, Xiyan 8 Jadlovská, Irena 7 Jiang, Zhaolin 7 Lebtahi, Leila 7 Mustafa, Octavian G. 7 Rost, Karla 7 Thome, Néstor 6 Baculíková, Blanka 6 Bogoya, Johan M. 6 Huang, Guang-Xin 6 Maksimenko, Egor A. 6 Pan, Victor Yakovlevich 6 Pinto, Manuel 6 Serra-Capizzano, Stefano 6 Shen, Weiping 6 Singh, Bhagat 6 Yin, Feng 6 Zhang, Lei 5 Agarwal, Ravi P. 5 Barnett, Stephen 5 Bini, Dario Andrea 5 Chang, Haixia 5 Chen, Guoliang 5 Dwivedi, Ravi 5 Heinig, Georg 5 Kailath, Thomas 5 Kitamura, Yuichi 5 Koo, Namjip 5 Li, Jiaofen 5 Naito, Manabu 5 Ng, Michael Kwok-Po 5 Zafer, Ağacık 4 Cecchi, Mariella 4 Chen, Shaozhu 4 Choi, Sungkyu 4 Dai, Lifang 4 Gover, Michael J. C. 4 Granata, Antonio 4 Greville, Thomas Nall Eden 4 Huang, Na 4 Li, Chong 4 Liang, Maolin 4 Peng, Zhenyun 4 Philos, Christos G. 4 Pituk, Mihály 4 Rogovchenko, Yuri V. 4 Sahai, Vivek 4 Tatar, Nasser-eddine 4 Vidal, Antonio Manuel 4 Xie, Yajun 4 Xu, Weiru 4 Yuan, Yongxin 4 Zheng, Yanpeng 3 Bohner, Martin J. 3 Chan, Raymond Hon-Fu 3 Delsarte, Philippe 3 Di Benedetto, Fabio 3 Dmytryshyn, Andrii R. 3 Elias, Uri 3 Gao, Zhen 3 Graef, John R. 3 Kassim, Mohammed Dahan 3 Li, Wen 3 Linzer, Elliot N. 3 Liu, Zhongyun 3 Luk, Franklin T. 3 Marini, Mauro 3 Medina, Rigoberto 3 Melman, Aaron 3 Migda, Janusz 3 Özbekler, Abdullah 3 Piramanantham, Veeraraghavan 3 Romero, Oscar 3 Saranya, K. 3 Sesana, Debora 3 Shon, Sugoog 3 Stević, Stevo 3 Stuart, Jeffrey L. 3 Swanson, Charles A. 3 Tunç, Ercan 3 Wang, Baoshan 3 Wen, Youwei 3 Wong, James S. W. 3 Zhang, Guofeng 2 Alonso, Pedro 2 Ammar, Gregory S. 2 Anderson, Brian David Outram 2 Badía, José M. 2 Bartušek, Miroslav 2 Batalshchikov, A. A. 2 Begović Kovač, Erna ...and 676 more Authors all top 5 Cited in 198 Serials 115 Linear Algebra and its Applications 42 Journal of Mathematical Analysis and Applications 40 Journal of Computational and Applied Mathematics 30 Applied Mathematics and Computation 24 Computers & Mathematics with Applications 16 Journal of Difference Equations and Applications 15 Linear and Multilinear Algebra 15 Proceedings of the American Mathematical Society 15 Applied Mathematics Letters 13 Journal of Differential Equations 11 Numerical Algorithms 11 Advances in Difference Equations 11 Nonlinear Analysis. Theory, Methods & Applications 9 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Czechoslovak Mathematical Journal 8 Abstract and Applied Analysis 7 Calcolo 7 Journal of Approximation Theory 6 Mathematics of Computation 6 Mathematica Slovaca 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Transactions of the American Mathematical Society 5 Circuits, Systems, and Signal Processing 5 Japan Journal of Industrial and Applied Mathematics 5 International Journal of Computer Mathematics 4 Numerische Mathematik 4 Mathematical and Computer Modelling 4 Applied Mathematical Modelling 4 Numerical Linear Algebra with Applications 4 Mathematical Problems in Engineering 4 Journal of Applied Mathematics 4 Journal of Physics A: Mathematical and Theoretical 4 Special Matrices 3 Analysis Mathematica 3 Journal of Computational Physics 3 Rocky Mountain Journal of Mathematics 3 Automatica 3 BIT 3 Computing 3 Glasgow Mathematical Journal 3 Applied Numerical Mathematics 3 SIAM Journal on Matrix Analysis and Applications 3 Computational Statistics and Data Analysis 3 Qualitative Theory of Dynamical Systems 3 The ANZIAM Journal 3 Journal of Applied Mathematics and Computing 3 Operators and Matrices 3 Journal of Nonlinear Science and Applications 2 Applicable Analysis 2 Artificial Intelligence 2 Archive for Rational Mechanics and Analysis 2 International Journal of Systems Science 2 Integral Equations and Operator Theory 2 Journal of Soviet Mathematics 2 Journal of Statistical Planning and Inference 2 SIAM Journal on Algebraic and Discrete Methods 2 Bulletin of the Iranian Mathematical Society 2 Constructive Approximation 2 Journal of Statistical Computation and Simulation 2 SIAM Journal on Scientific Computing 2 Applied and Computational Harmonic Analysis 2 Electronic Journal of Differential Equations (EJDE) 2 Turkish Journal of Mathematics 2 Finite Fields and their Applications 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 ELA. The Electronic Journal of Linear Algebra 2 Parallel Algorithms and Applications 2 Journal of Shanghai University 2 Mathematical Modelling and Analysis 2 Applied Mathematics E-Notes 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Nonautonomous Dynamical Systems 1 American Mathematical Monthly 1 The American Statistician 1 Bulletin of the Australian Mathematical Society 1 Classical and Quantum Gravity 1 Computer Methods in Applied Mechanics and Engineering 1 Inverse Problems 1 Information Processing Letters 1 Israel Journal of Mathematics 1 Journal of Engineering Mathematics 1 Lithuanian Mathematical Journal 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 Reports on Mathematical Physics 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Acta Scientiarum Mathematicarum 1 Advances in Mathematics 1 Archiv der Mathematik 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Combinatorial Theory. Series A 1 Journal of Computer and System Sciences 1 Journal of Econometrics 1 Journal of Functional Analysis 1 Journal of Multivariate Analysis 1 Journal of Number Theory 1 Meccanica 1 Numerical Functional Analysis and Optimization 1 Proceedings of the Edinburgh Mathematical Society. Series II ...and 98 more Serials all top 5 Cited in 51 Fields 262 Linear and multilinear algebra; matrix theory (15-XX) 246 Numerical analysis (65-XX) 168 Ordinary differential equations (34-XX) 62 Difference and functional equations (39-XX) 44 Operator theory (47-XX) 38 Statistics (62-XX) 25 Partial differential equations (35-XX) 20 Approximations and expansions (41-XX) 17 Computer science (68-XX) 16 Real functions (26-XX) 15 Number theory (11-XX) 15 Special functions (33-XX) 12 Probability theory and stochastic processes (60-XX) 12 Operations research, mathematical programming (90-XX) 10 Systems theory; control (93-XX) 9 Combinatorics (05-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 7 Integral equations (45-XX) 7 Quantum theory (81-XX) 7 Information and communication theory, circuits (94-XX) 6 Sequences, series, summability (40-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Functions of a complex variable (30-XX) 5 Differential geometry (53-XX) 5 Mechanics of particles and systems (70-XX) 5 Fluid mechanics (76-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Mechanics of deformable solids (74-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Algebraic geometry (14-XX) 2 General and overarching topics; collections (00-XX) 2 Field theory and polynomials (12-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 2 Potential theory (31-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Geometry (51-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 \(K\)-theory (19-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) Citations by Year