Korovkin theorems and linear positive Gram matrix algebra approximations of Toeplitz matrices

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

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

[3]  Gian-Carlo Rota,et al.  Linear Operators and Approximation Theory. , 1965 .

[4]  I. P. Natanson.  Constructive function theory , 1964 .

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

[6]  On some new Banach algebras and Wiener-Levy type theorems for Fourier series and integrals , 1970 .

[7]  I. Gohberg,et al.  Convolution Equations and Projection Methods for Their Solution , 1974 .

[8]  Alan V. Oppenheim,et al.  Applications of digital signal processing , 1978 .

[9]  Dario Bini,et al.  SPECTRAL AND COMPUTATIONAL PROPERTIES OF BAND SYMMETRIC TOEPLITZ MATRICES , 1983 .

[10]  Walter Gautschi.  The condition of Vandermonde-like matrices involving orthogonal polynomials☆ , 1983 .

[11]  Gene H. Golub,et al.  Matrix computations , 1983 .

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

[13]  G. Strang.  A proposal for toeplitz matrix calculations , 1986 .

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

[15]  T. Chan.  An Optimal Circulant Preconditioner for Toeplitz Systems , 1988 .

[16]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[17]  Harold Widom.  On the Singular Values of Toeplitz Matrices , 1989 .

[18]  Dario Bini,et al.  A new preconditioner for the parallel solution of positive definite Toeplitz systems , 1990, SPAA '90.

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

[20]  R. Chan,et al.  The circulant operator in the banach algebra of matrices , 1991 .

[21]  R. Chan.  Toeplitz Preconditioners for Toeplitz Systems with Nonnegative Generating Functions , 1991 .

[22]  R. Chan,et al.  Circulant preconditioners constructed from kernels , 1992 .

[23]  Raymond H. Chan,et al.  Circulant preconditioners for Toeplitz matrices with piecewise continuous generating functions , 1992 .

[24]  Thomas Huckle,et al.  Circulant and Skewcirculant Matrices for Solving Toeplitz Matrix Problems , 1992, SIAM J. Matrix Anal. Appl..

[25]  Paola Favati,et al.  On a matrix algebra related to the discrete Hartley transform , 1993 .

[26]  Stefano Serra,et al.  Preconditioning strategies for asymptotically ill-conditioned block Toeplitz systems , 1994 .

[27]  J. Nagy,et al.  Circulant Preconditioned Toeplitz Least Squares Iterations , 1994, SIAM J. Matrix Anal. Appl..

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

[29]  Eugene E. Tyrtyshnikov,et al.  Circulant preconditioners with unbounded inverses , 1995 .

[30]  Fabio Di Benedetto,et al.  Analysis of Preconditioning Techniques for Ill-Conditioned Toeplitz Matrices , 1995, SIAM J. Sci. Comput..

[31]  T. Kailath,et al.  Displacement structure approach to discrete-trigonometric-transform based preconditioners of G.Strang type and of T.Chan type , 1996 .

[32]  J. Nagy,et al.  Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques , 1996 .

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

[34]  Stefano Serra.  Preconditioning Strategies for Hermitian Toeplitz Systems with Nondefinite Generating Functions , 1996 .

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

[36]  Stefano Serra.  The extension of the concept of the generating function to a class of preconditioned Toeplitz matrices , 1997 .

[37]  Stefano Serra,et al.  Optimal, quasi-optimal and superlinear band-Toeplitz preconditioners for asymptotically ill-conditioned positive definite Toeplitz systems , 1997 .

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

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

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

[41]  Georg Heinig,et al.  Representations of Toeplitz-plus-Hankel matrices using trigonometric transformations with application to fast matrix-vector multiplication , 1998 .

[42]  Stefano Serra,et al.  On the extreme eigenvalues of hermitian (block) toeplitz matrices , 1998 .

[43]  Stefano Serra Capizzano,et al.  Toeplitz Preconditioners Constructed from Linear Approximation Processes , 1999, SIAM J. Matrix Anal. Appl..

[44]  Beatrice Meini,et al.  Effective Methods for Solving Banded Toeplitz Systems , 1999, SIAM J. Matrix Anal. Appl..

[45]  Stefano Serra.  How to Choose the Best Iterative Strategy for Symmetric Toeplitz Systems , 1999 .

[46]  Stefano Serra,et al.  A Korovkin-type theory for finite Toeplitz operators via matrix algebras , 1999 .

[47]  Stefano Serra Capizzano,et al.  A unifying approach to abstract matrix algebra preconditioning , 1999, Numerische Mathematik.