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A Lanczos‐type algorithm for the QR factorization of regular Cauchy matrices
Author(s) -
Fasino Dario,
Gemignani Luca
Publication year - 2002
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.275
Subject(s) - mathematics , cauchy distribution , matrix (chemical analysis) , factorization , lanczos resampling , algorithm , combinatorics , algebra over a field , pure mathematics , eigenvalues and eigenvectors , mathematical analysis , materials science , physics , quantum mechanics , composite material
We present a fast algorithm for computing the QR factorization of Cauchy matrices with real nodes. The algorithm works for almost any input matrix, does not require squaring the matrix, and fully exploits the displacement structure of Cauchy matrices. We prove that, if the determinant of a certain semiseparable matrix is non‐zero, a three term recurrence relation among the rows or columns of the factors exists. Copyright © 2002 John Wiley & Sons, Ltd.