Constructive methods for factorization of matrix-functions

被引：44

作者：

Rogosin, Sergei ^{[1
,2
]}

Mishuris, Gennady ^{[1
]}

机构：

[1] Aberystwyth Univ, Penglais, Aberystwyth SY23 2BZ, Dyfed, Wales

[2] Belarusian State Univ, Nezavisimosti Ave 4, Minsk 220030, BELARUS

来源：

IMA JOURNAL OF APPLIED MATHEMATICS | 2016年 / 81卷 / 02期

关键词：

matrix-functions; factorization; constructive methods; WIENER-HOPF FACTORIZATION; PARTIAL INDEXES; GENERALIZED FACTORIZATION; CANONICAL FACTORIZATION; SPECTRAL FACTORIZATION; EXPLICIT FACTORIZATION; APPROXIMATE FACTORIZATION; PREDICTION THEORY; EQUATIONS; RIEMANN;

D O I：

10.1093/imamat/hxv038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A survey of constructive methods for the factorization of n x n matrix-functions is presented. The importance of these methods for theoretical and practical applications is singled out. Several classes of matrices are considered which are factorized by the proper technique. The perspective of the constructive methods and procedures is discussed and open questions are formulated.

引用

页码：365 / 391

页数：27

共 50 条

[31] Wiener-Hopf Factorization of a Class of Matrix Functions and Corona Theorem [J].

GUO Guoan .

Wuhan University Journal of Natural Sciences, 2009, 14 (01) :1-5

[32] A New Method of Matrix Spectral Factorization [J].

Janashia, Gigla ;

Lagvilava, Edem ;

Ephremidze, Lasha .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (04) :2318-2326

[33] About explicit factorization of some classes of non-rational matrix functions [J].

Conceicao, Ana C. ;

Kravchenko, Viktor G. .

MATHEMATISCHE NACHRICHTEN, 2007, 280 (9-10) :1022-1034

[34] Factorization of block triangular matrix functions in Wiener algebras on ordered abelian groups [J].

van der Mee, CVM ;

Rodman, L ;

Spitkovsky, IM ;

Woerdeman, HJ .

CURRENT TRENDS IN OPERATOR THEORY AND ITS APPLICATIONS, 2004, 149 :441-465

[35] The corona theorem and the existence of canonical factorization of triangular AP-matrix functions [J].

Bastos, MA ;

Karlovich, YI ;

dos Santos, AF ;

Tishin, PM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 223 (02) :494-522

[36] A Class of Hölder Matrix Functions of the Second Order Admitting Effective Factorization [J].

S. N. Kiyasov .

Russian Mathematics, 2022, 66 :56-61

[37] Comparison of methods for evaluating functions of a matrix exponential [J].

Ashi, H. A. ;

Cummings, L. J. ;

Matthews, P. C. .

APPLIED NUMERICAL MATHEMATICS, 2009, 59 (3-4) :468-486

[38] Zerofinding of analytic functions by structured matrix methods [J].

Gemignani, Luca .

PANORAMA OF MATHEMATICS: PURE AND APPLIED, 2016, 658 :47-66

[39] Canonical factorization of rational matrix functions. A note on a paper by P. Dewilde [J].

Frazho, A. E. ;

Kaashoek, M. A. .

INDAGATIONES MATHEMATICAE-NEW SERIES, 2012, 23 (04) :1154-1164

[40] Extended and rational Hessenberg methods for the evaluation of matrix functions [J].

Ramezani, Z. ;

Toutounian, F. .

BIT NUMERICAL MATHEMATICS, 2019, 59 (02) :523-545

← 1 2 3 4 5 →