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

[21]

Henrici P., 1962, Numer. Math, V4, P24, DOI 10.1007/BF01386294

[22]

HIGHAM NJ, 1989, INST MATH C, V22, P1

[23] PARALLELIZABLE RESTARTED ITERATIVE METHODS FOR NONSYMMETRIC LINEAR-SYSTEMS .1. THEORY [J].

JOUBERT, WD ;

CAREY, GF .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1992, 44 (1-4) :243-267

[24] PARALLELIZABLE RESTARTED ITERATIVE METHODS FOR NONSYMMETRIC LINEAR-SYSTEMS .2. PARALLEL IMPLEMENTATION [J].

JOUBERT, WD ;

CAREY, GF .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1992, 44 (1-4) :269-290

[25] Structured eigenvalue condition numbers [J].

Karow, Michael ;

Kressner, Daniel ;

Tisseur, Francoise .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2006, 28 (04) :1052-1068

[26] AN ATTAINABLE LOWER-BOUND FOR THE BEST NORMAL APPROXIMATION [J].

LASZLO, L .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1994, 15 (03) :1035-1043

[27] Best available bounds for departure from normality [J].

Lee, SL .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1996, 17 (04) :984-991

[28] ON THE SPECTRAL PROPERTIES OF MATRICES ASSOCIATED WITH TREND FILTERS [J].

Luati, Alessandra ;

Proietti, Tommaso .

ECONOMETRIC THEORY, 2010, 26 (04) :1247-1261

[29] A truncated projected SVD method for linear discrete ill-posed problems [J].

Morigi, Serena ;

Reichel, Lothar ;

Sgallari, Fiorella .

NUMERICAL ALGORITHMS, 2006, 43 (03) :197-213

[30]

Noschese S, 2007, ELECTRON T NUMER ANA, V28, P65

← 1 2 3 4 5 →