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Functions of a matrix and Krylov matrices

✍ Scribed by Hongguo Xu

Book ID
104038522
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
247 KB
Volume
434
Category
Article
ISSN
0024-3795

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✦ Synopsis

For a given nonderogatory matrix A, formulas are given for functions of A in terms of Krylov matrices of A. Relations between the coefficients of a polynomial of A and the generating vector of a Krylov matrix of A are provided. With the formulas, linear transformations between Krylov matrices and functions of A are introduced, and associated algebraic properties are derived. Hessenberg reduction forms are revisited equipped with appropriate inner products and related properties and matrix factorizations are given.

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