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

[1]

[Anonymous], 1965, The algebraic eigenvalue problem

[2]

[Anonymous], 2003, ITERATIVE METHODS SP, DOI DOI 10.1137/1.9780898718003

[3] Single-input eigenvalue assignment algorithms: A close look [J].

Arnold, M ;

Datta, BN .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1998, 19 (02) :444-467

[4] A NEWTON BASIS GMRES IMPLEMENTATION [J].

BAI, Z ;

HU, D ;

REICHEL, L .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1994, 14 (04) :563-581

[5]

BOTTCHER A, 2005, SPECTRAL PROPERTIES

[6] Invertible smoothing preconditioners for linear discrete ill-posed problems [J].

Calvetti, D ;

Reichel, L ;

Shuibi, A .

APPLIED NUMERICAL MATHEMATICS, 2005, 54 (02) :135-149

[7]

CALVETTI D, 1993, NUMERICAL LINEAR ALGEBRA, P31

[8] Robust partial pole assignment for vibrating systems with aerodynamic effects [J].

Datta, Biswa N. ;

Lin, Wen-Wei ;

Wang, Jenn-Nan .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (12) :1979-1984

[9] A solution of the affine quadratic inverse eigenvalue problem [J].

Datta, Biswa Nath ;

Sokolov, Vadim .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (07) :1745-1760

[10] ARNOLDI METHODS FOR LARGE SYLVESTER-LIKE OBSERVER MATRIX EQUATIONS, AND AN ASSOCIATED ALGORITHM FOR PARTIAL SPECTRUM ASSIGNMENT [J].

DATTA, BN ;

SAAD, Y .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 154 :225-244

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