Tridiagonal Toeplitz matrices: properties and novel applications

被引：166

作者：

Noschese, Silvia ^{[1
]}

Pasquini, Lionello ^{[1
]}

Reichel, Lothar ^{[2
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat Guido Castelnuovo, I-00185 Rome, Italy

[2] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2013年 / 20卷 / 02期

基金：

美国国家科学基金会;

关键词：

eigenvalues; conditioning; Toeplitz matrix; matrix nearness problem; distance to normality; inverse eigenvalue problem; Krylov subspace bases; Tikhonov regularization; NONSYMMETRIC LINEAR-SYSTEMS; RESTARTED ITERATIVE METHODS; CONDITION NUMBERS; EIGENVALUES; ASSIGNMENT; ALGORITHM;

D O I：

10.1002/nla.1811

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The eigenvalues and eigenvectors of tridiagonal Toeplitz matrices are known in closed form. This property is in the first part of the paper used to investigate the sensitivity of the spectrum. Explicit expressions for the structured distance to the closest normal matrix, the departure from normality, and the E-pseudospectrum are derived. The second part of the paper discusses applications of the theory to inverse eigenvalue problems, the construction of Chebyshev polynomial-based Krylov subspace bases, and Tikhonov regularization. Copyright (c) 2012 John Wiley & Sons, Ltd.

引用

页码：302 / 326

页数：25

共 44 条

[31] Eigenvalue patterned condition numbers: Toeplitz and Hankel cases [J].

Noschese, S. ;

Pasquini, L. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 206 (02) :615-624

[32] Eigenvalue condition numbers: Zero-structured versus traditional [J].

Noschese, S ;

Pasquini, L .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 185 (01) :174-189

[33] The structured distance to normality of banded Toeplitz matrices [J].

Noschese, Silvia ;

Reichel, Lothar .

BIT NUMERICAL MATHEMATICS, 2009, 49 (03) :629-640

[34]

Philippe B, APPL NUMERI IN PRESS

[35] EIGENVALUES AND PSEUDO-EIGENVALUES OF TOEPLITZ MATRICES [J].

REICHEL, L ;

TREFETHEN, LN .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 162 :153-185

[36]

Reichel L, 2008, ELECTRON T NUMER ANA, V33, P63

[37]

Sidje RB, 1997, NUMER LINEAR ALGEBR, V4, P305, DOI 10.1002/(SICI)1099-1506(199707/08)4:4<305::AID-NLA104>3.3.CO

[38]

2-4

[39]

SMITH GD, 1978, NUMERICAL SOLUTION P

[40]

Smithies L, 2010, ELECTRON T NUMER ANA, V36, P99

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