, Stability analysis of a general Toeplitz systems solver, Numerical Algorithms 10 (1995), 225--244.  Home/Search   Document Details and Download   Summary   Related Articles

....numerical problem [5, 67] 6.1. Use of the semi normal equations. It can be shown that, provided the Cholesky downdates are implemented in a certain way (analogous to the condition for the stability of the generalized Schur algorithm) the BBH algorithm computes U in a weakly stable manner [7]. In fact, the computed upper triangular matrix U is about as good as can be obtained by performing a Cholesky factorization of T T T , so kT T T Gamma U T Uk=kT T Tk = Om ( Thus, by solving U T Ux = T T b (the so called semi normal equations) we have a weakly ....

....involves embedding the n Theta n matrix T in a 2n Theta 2n matrix T T T T T T 0 ; the constant factors in the operation count are large: 59n 2 O(n log n) which should be compared to 8n 2 O(n log n) for BBH and the semi normal equations. These operation counts apply for m = n: see [7] for operation counts of various algorithms when m n. Thus, although the embedding approach is elegant and leads to interesting (and in some cases stable) O(n 2 ) algorithms, a penalty is the significant increase in the constant factors. This is analogous to the penalty paid by the GKO ....

, Stability analysis of a general Toeplitz systems solver, Numerical Algorithms 10 (1995), 225--244.

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