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Solving Toeplitz and Vandermondelike Linear Systems with Large Displacement Rank
, 2007
"... Linear systems with structures such as Toeplitz, Vandermonde or Cauchylikeness can be solved in O˜(α 2 n) operations, where n is the matrix size, α is its displacement rank, and O ˜ denotes the omission of logarithmic factors. We show that for Toeplitzlike and Vandermondelike matrices, this cos ..."
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Cited by 4 (2 self)
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Linear systems with structures such as Toeplitz, Vandermonde or Cauchylikeness can be solved in O˜(α 2 n) operations, where n is the matrix size, α is its displacement rank, and O ˜ denotes the omission of logarithmic factors. We show that for Toeplitzlike and Vandermondelike matrices
The structured sensitivity of Vandermondelike systems
 Numer. Math
, 1992
"... Summary. We consider a general class of structured matrices that includes (possibly confluent) Vandermonde and Vandermondelike matrices. Here the entries in the matrix depend nonlinearly upon a vector of parameters. We define condition numbers that measure the componentwise sensitivity of the ass ..."
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Cited by 5 (1 self)
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Summary. We consider a general class of structured matrices that includes (possibly confluent) Vandermonde and Vandermondelike matrices. Here the entries in the matrix depend nonlinearly upon a vector of parameters. We define condition numbers that measure the componentwise sensitivity
A SUPERFAST ALGORITHM FOR TOEPLITZ SYSTEMS OF LINEAR EQUATIONS
"... In this paper we develop a new superfast solver for Toeplitz systems of linear equations. To solve Toeplitz systems many people use displacement equation methods. With displacement structures, Toeplitz matrices can be transformed into Cauchylike matrices using the FFT or other trigonometric transf ..."
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Cited by 24 (4 self)
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In this paper we develop a new superfast solver for Toeplitz systems of linear equations. To solve Toeplitz systems many people use displacement equation methods. With displacement structures, Toeplitz matrices can be transformed into Cauchylike matrices using the FFT or other trigonometric
on a Tridiagonal Toeplitz Linear System
, 2007
"... The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric linear system Ax = b. But its convergence analysis is a rather difficult task in general. A commonly used approach is to diagonalize A = XΛX −1 and then separate the study of GMRES convergence behavior into optimiz ..."
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Cited by 1 (1 self)
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The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric linear system Ax = b. But its convergence analysis is a rather difficult task in general. A commonly used approach is to diagonalize A = XΛX −1 and then separate the study of GMRES convergence behavior
QRfactorization of displacement structured matrices using a rank structured matrix approach
, 2007
"... A general scheme is proposed for computing the QRfactorization of certain displacement structured matrices, including Cauchylike, Vandermondelike, Toeplitzlike and Hankellike matrices, hereby extending some earlier work for the QRfactorization of the Cauchy matrix. The algorithm employs a cha ..."
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A general scheme is proposed for computing the QRfactorization of certain displacement structured matrices, including Cauchylike, Vandermondelike, Toeplitzlike and Hankellike matrices, hereby extending some earlier work for the QRfactorization of the Cauchy matrix. The algorithm employs a
Algorithms for rankdeficient and illconditioned Toeplitz leastsquares and QR factorization
"... In this paper we present two algorithms  one to compute the QR factorization of nearly rankdeficient Toeplitz and block Toeplitz matrices and the other to compute the solution of a severely illconditioned Toeplitz leastsquares problem. The first algorithm is based on adapting the generalized Sch ..."
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Schur algorithm to Cauchylike matrices and has some rankrevealing capability. The other algorithm is based on adapting the augmented systems method to Toeplitz matrices. This algorithm does not suffer from the numerical inaccuracy of most Levinson and Schurbased schemes proposed in the literature
we optimize Toeplitz/Hankel computations
 in Proceedings of the Fifth International Workshop on Computer Algebra in Scientific Computing (CASC 2002
, 2002
"... Abstract. The classical and intensively studied problem of solving a Toeplitz/Hankel linear system of equations is omnipresent in computations in sciences, engineering and communication. Its equivalent formulations include computing polynomial gcd and lcm, Padé approximation, and BerlekampMassey’s ..."
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Cited by 4 (2 self)
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Abstract. The classical and intensively studied problem of solving a Toeplitz/Hankel linear system of equations is omnipresent in computations in sciences, engineering and communication. Its equivalent formulations include computing polynomial gcd and lcm, Padé approximation, and Berlekamp
Results 1  10
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795