A proposal for toeplitz matrix calculations
Studies in Applied Mathematics
FORTRAN subroutines for general Toeplitz systems
ACM Transactions on Mathematical Software (TOMS)
Optimal and superoptimal circulant preconditioners
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Fast reliable algorithms for matrices with structure
Fast reliable algorithms for matrices with structure
A Method for Generating Infinite Positive Self-adjoint Test Matrices and Riesz Bases
SIAM Journal on Matrix Analysis and Applications
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
A fast solver for linear systems with displacement structure
Numerical Algorithms
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The full exploitation of the structure of large scale algebraic problems is often crucial for their numerical solution. Matlab is a computational environment which supports sparse matrices, besides full ones, and allows one to add new types of variables (classes) and define the action of arithmetic operators and functions on them. The smt toolbox for Matlab introduces two new classes for circulant and Toeplitz matrices, and implements optimized storage and fast computational routines for them, transparently to the user. The toolbox, available in Netlib, is intended to be easily extensible, and provides a collection of test matrices and a function to compute three circulant preconditioners, to speed up iterative methods for linear systems. Moreover, it incorporates a simple device to add to the toolbox new routines for solving Toeplitz linear systems.