Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices. II: Algorithms
In continuation of the authors' earlier paper [part I, ibid. 254, 193-226 (1997; Zbl 0872.65021)] fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. Cauchy matrices have the property that permutations of columns and rows preserve the Cauchy structure. This property provides additional freedom in how matrix decomposition algorithms based on Gaussian elimination can be applied. It turns out that instead of dealing with Toeplitz and Toeplitz-plus-Hankel matrices, it is worthwhile, from the numerical point of view, to deal with the corresponding Cauchy matrices. It is shown that the combination of transformation pivoting techniques leads to faster algorithms for infinite Toeplitz and Toeplitz-plus-Hankel matrices that are more stable than the classical ones.
scientific article; zbMATH DE number 1354769
scientific article