Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices II. Algorithms
Georg Heinig, Adam W. Bojańczyk · Linear Algebra and its Applications · 1998
This paper is a continuation of [G. Heinig, A. Bojanczyk, Linear Algebra Appl. 254 (1997) 193–226] where transformations mapping Toeplitz and Toeplitz-plus-Hankel matrices into generalized Cauchy matrices were studied. In the present paper fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. It is shown that the combination of transformation pivoting techniques leads to algorithms for indefinite Toeplitz and Toeplitz-plus-Hankel matrices that are more stable than the classical ones. Special attention is paid to the symmetric and hermitian cases.