The GLT class as a generalized Fourier analysis and applications

[1]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[2]  Stefano Serra Capizzano,et al.  On the Asymptotic Spectrum of Finite Element Matrix Sequences , 2007, SIAM J. Numer. Anal..

[3]  Sverker Holmgren,et al.  Can One Hear the Composition of a Drum? , 2006 .

[4]  Albrecht Böttcher,et al.  On the Problem of Testing the Structure of a Matrix by Displacement Operations , 2006, SIAM J. Numer. Anal..

[5]  S. Capizzano,et al.  The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences , 2005, J. Approx. Theory.

[6]  V. Ivrii.  Sharp Spectral Asymptotics for Operators with Irregular Coefficients. V. Multidimensional Schroedinger operator with a strong magnetic field. Non-Full-rank case , 2005, math/0510327.

[7]  Gene H. Golub,et al.  How to Deduce a Proper Eigenvalue Cluster from a Proper Singular Value Cluster in the Nonnormal Case , 2005, SIAM J. Matrix Anal. Appl..

[8]  H. Widom,et al.  From Toeplitz Eigenvalues through Green’s Kernels to Higher-order Wirtinger-Sobolev Inequalities , 2004, math/0412269.

[9]  Wolfgang Joppich,et al.  Practical Fourier Analysis for Multigrid Methods , 2004 .

[10]  A. Böttcher.  The Constants in the Asymptotic Formulas by Rambour and Seghier for Inverses of Toeplitz Matrices , 2004 .

[11]  L. Trefethen,et al.  Wave packet pseudomodes of twisted Toeplitz matrices , 2004 .

[12]  Gabriele Steidl,et al.  Fast convolution with radial kernels at nonequispaced knots , 2004, Numerische Mathematik.

[13]  Stefano Serra Capizzano,et al.  Matrix algebra preconditioners for multilevel Toeplitz systems do not insure optimal convergence rate , 2004, Theor. Comput. Sci..

[14]  Peter B. Gilkey,et al.  Asymptotic Formulae in Spectral Geometry , 2003 .

[15]  Stefano Serra Capizzano,et al.  Analysis of preconditioning strategies for collocation linear systems , 2003 .

[16]  Stefano Serra Capizzano,et al.  How to prove that a preconditioner cannot be superlinear , 2003, Math. Comput..

[17]  S. Serra Capizzano,et al.  Generalized locally Toeplitz sequences: spectral analysis and applications to discretized partial differential equations , 2003 .

[18]  Victor Ivrii,et al.  Sharp Spectral Asymptotics for Operators with Irregular Coefficients. I. Pushing the Limits , 2003 .

[19]  Stefano Serra Capizzano,et al.  Convergence analysis of two-grid methods for elliptic Toeplitz and PDEs Matrix-sequences , 2002, Numerische Mathematik.

[20]  MILAN HLADNIK,et al.  Fat Diagonals and Fourier Analysis , 2002, SIAM J. Matrix Anal. Appl..

[21]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[22]  S. Capizzano.  Matrix algebra preconditioners for multilevel Toeplitz matrices are not superlinear , 2002 .

[23]  G. H. Golub,et al.  A Stochastic Approach to Error Estimates for Iterative Linear Solvers: Part 1 , 2001 .

[24]  Stefano Serra Capizzano,et al.  Asymptotic Zero Distribution of Orthogonal Polynomials with Discontinuously Varying Recurrence Coefficients , 2001, J. Approx. Theory.

[25]  S. Serra Capizzano,et al.  Distribution results on the algebra generated by Toeplitz sequences: a finite-dimensional approach , 2001 .

[26]  J. Fleckinger-Pellé.  THE VIBRATIONS OF A DRUM WITH FRACTAL BOUNDARY , 2001 .

[27]  Stefano Serra Capizzano,et al.  Korovkin tests, approximation, and ergodic theory , 2000, Math. Comput..

[28]  Rajendra Bhatia,et al.  Pinching, Trimming, Truncating, and Averaging of Matrices , 2000, Am. Math. Mon..

[29]  Per Lötstedt.  Convergence analysis of iterative methods by pseudodifference operators , 2000 .

[30]  Paolo Tilli,et al.  Asymptotic Spectra of Hermitian Block Toeplitz Matrices and Preconditioning Results , 2000, SIAM J. Matrix Anal. Appl..

[31]  Paolo Tilli,et al.  Some Results on Complex Toeplitz Eigenvalues , 1999 .

[32]  Stefano Serra Capizzano,et al.  Spectral and structural analysis of high precision finite difference matrices for elliptic operators , 1999 .

[33]  S. Serra,et al.  Spectral and Computational Analysis of Block Toeplitz Matrices Having Nonnegative Definite Matrix-Valued Generating Functions , 1999 .

[34]  Paolo Tilli,et al.  A note on the spectral distribution of toeplitz matrices , 1998 .

[35]  A. Böttcher,et al.  Introduction to Large Truncated Toeplitz Matrices , 1998 .

[36]  Stefano Serra Capizzano,et al.  An ergodic theorem for classes of preconditioned matrices , 1998 .

[37]  Paolo Tilli,et al.  Locally Toeplitz sequences: spectral properties and applications , 1998 .

[38]  Dianne P. O'Leary,et al.  Restoring Images Degraded by Spatially Variant Blur , 1998, SIAM J. Sci. Comput..

[39]  Eugene E. Tyrtyshnikov,et al.  Spectra of multilevel toeplitz matrices: Advanced theory via simple matrix relationships , 1998 .

[40]  R. Bhatia.  Matrix Analysis , 1996 .

[41]  Raymond H. Chan,et al.  Conjugate Gradient Methods for Toeplitz Systems , 1996, SIAM Rev..

[42]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .

[43]  P. Tilli.  Singular values and eigenvalues of non-hermitian block Toeplitz matrices , 1996 .

[44]  Sverker Holmgren,et al.  Semicirculant Solvers and Boundary Corrections for First-Order Partial Differential Equations , 1996, SIAM J. Sci. Comput..

[45]  H. Kreiss,et al.  Time-Dependent Problems and Difference Methods , 1996 .

[46]  Ali H. Sayed,et al.  Displacement Structure: Theory and Applications , 1995, SIAM Rev..

[47]  R. Tibshirani,et al.  An Introduction to the Bootstrap , 1995 .

[48]  E. E. Tyrtyshnikov.  Influence of matrix operations on the distribution of Eigenvalues and singular values of Toeplitz matrices , 1994 .

[49]  David L. Webb,et al.  Isospectral plane domains and surfaces via Riemannian orbifolds , 1992 .

[50]  Stefano Serra,et al.  Multigrid methods for toeplitz matrices , 1991 .

[51]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations , 1989 .

[52]  TONY F. CHAN,et al.  Fourier Analysis of Iterative Methods for Elliptic pr , 1989, SIAM Rev..

[53]  F. Avram.  On bilinear forms in Gaussian random variables and Toeplitz matrices , 1988 .

[54]  Edward B. Saff,et al.  On Clenshaws's method and a generalisation to faber series , 1987 .

[55]  Seymour V. Parter,et al.  On the distribution of the singular values of Toeplitz matrices , 1986 .

[56]  O. Axelsson,et al.  On the rate of convergence of the preconditioned conjugate gradient method , 1986 .

[57]  Georg Heinig,et al.  Algebraic Methods for Toeplitz-like Matrices and Operators , 1984 .

[58]  Anne Greenbaum,et al.  Analysis of a Multigrid Method as an Iterative Technique for Solving Linear Systems , 1984 .

[59]  D. Jackson,et al.  The theory of approximation , 1982 .

[60]  V. Guillemin,et al.  The Spectral Theory of Toeplitz Operators. , 1981 .

[61]  H. Widom.  Szegö's limit theorem: The higher-dimensional matrix case☆ , 1980 .

[62]  H. Widom.  Asymptotic behavior of block Toeplitz matrices and determinants. II , 1974 .

[63]  W. Rudin.  Real and complex analysis , 1968 .

[64]  M. Kac.  Can One Hear the Shape of a Drum , 1966 .

[65]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[66]  Peter D. Lax,et al.  On the stability of difference approximations to solutions of hyperbolic equations with variable coefficients , 1961 .

[67]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[68]  Gene H. Golub,et al.  Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation , 2005, Numerische Mathematik.

[69]  Stefano Serra Capizzano,et al.  V-cycle Optimal Convergence for Certain (Multilevel) Structured Linear Systems , 2004, SIAM J. Matrix Anal. Appl..

[70]  Michael Frazier,et al.  Studies in Advanced Mathematics , 2004 .

[71]  Paolo Tilli,et al.  On unitarily invariant norms of matrix-valued linear positive operators , 2002 .

[72]  Thomas Huckle,et al.  Multigrid Preconditioning and Toeplitz Matrices , 2002 .

[73]  Beatrice Meini,et al.  Approximate displacement rank and applications , 2001 .

[74]  Stefano Serra Capizzano,et al.  A note on the asymptotic spectra of finite difference discretizations of second order elliptic partial differential equations , 2000 .

[75]  Stefano Serra-Capizzano,et al.  Positive representation formulas for finite difference discretizations of (elliptic) second order PDEs , 1999 .

[76]  Stefano Serra,et al.  The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems , 1999 .

[77]  Stefano Serra,et al.  Asymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices , 1999 .

[78]  Mario Bertero,et al.  Introduction to Inverse Problems in Imaging , 1998 .

[79]  E. E. Tyrtyshnikov.  A unifying approach to some old and new theorems on distribution and clustering , 1996 .

[80]  Raymond H. Chan,et al.  Circulant preconditioners for elliptic problems , 1992 .

[81]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[82]  J. W. Ruge,et al.  4. Algebraic Multigrid , 1987 .

[83]  G. Grubb.  On the Functional Calculus of Pseudo-Differential Boundary Problems , 1984 .

[84]  G. Golub.  Matrix computations , 1983 .

[85]  A. Brandt.  Guide to multigrid development , 1982 .

[86]  Robert T. Seeley,et al.  Complex powers of an elliptic operator , 1967 .

[87]  L. Hörmander,et al.  Pseudo-differential Operators and Non-elliptic Boundary Problems , 1966 .

[88]  Isidore Isaac Hirschman,et al.  Studies in real and complex analysis , 1965 .

[89]  Burton Wendroff,et al.  On the stability of difference schemes , 1962 .

[90]  Seymour V. Parter,et al.  On the eigenvalues of certain generalisations of Toeplitz matrices , 1962 .

[91]  G. Szegő,et al.  On the Eigen-Values of Certain Hermitian Forms , 1953 .