Stable factorization for Hankel and Hankel-like matrices

This paper gives fast O(n(2)) algorithms for the factorization of positive- definite and indefinite Hank-el matrices. The algorithms are based on the c oncept of displacement structure and are valid for the more general class o f Hank-el-like matrices. The positive-definite algorithm is proven to be ba ckward stable. The indefinite algorithm uses a look-ahead step that is natu rally suggested by displacement approach. Our error analysis suggests a new criterion for the size of the look-ahead step and our numerical experiment s suggest that the use of the new criterion allows Lis to ensure numerical stability in practice. Copyright (C) 2001 John Wiley & Sons, Ltd.