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Topics in the numerical linear algebra of Toeplitz and Hankel matrices
Author(s) -
Böttcher Albrecht,
Rost Karla
Publication year - 2005
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201490009
Subject(s) - toeplitz matrix , algebra over a field , linear algebra , mathematics , hankel matrix , numerical linear algebra , pure mathematics , linear system , mathematical analysis , geometry
Abstract This is an introduction to some aspects of the numerical linear algebra of large matrices with Toeplitz, Hankel, and Toeplitz‐plus‐Hankel structures. The concrete topics we have selected are determined by our preferences and by work we have participated in. We give an introduction to the symbol calculus, we touch exact and asymptotic formulas for inverses, including the notion of a Bezoutian, we consider eigenvalues, pseudospectra, eigenvectors, and condition numbers, and we embark on the fast solution of Toeplitz systems. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)