Numerical Stability of Some Fast Algorithms for Structured Matrices Export

@misc{citeulike:5800762, abstract = {We consider the numerical stability/instability of fast algorithms for solving systems of linear equations or linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. In particular, we consider algorithms which incorporate pivoting without destroying the structure, such as the Gohberg-Kailath-Olshevsky (GKO) algorithm, and describe some recent results on the stability of these algorithms. We also compare these results with the corresponding stability results for algorithms based on the semi-normal equations and for the well known algorithms of Schur/Bareiss and Levinson.}, author = {Brent, Richard P.}, citeulike-article-id = {5800762}, keywords = {linear\_algebra, matrix}, posted-at = {2009-09-17 23:56:54}, priority = {2}, title = {Numerical Stability of Some Fast Algorithms for Structured Matrices} }

TY - GEN ID - citeulike:5800762 L3 - citeulike-article-id:5800762 N2 - We consider the numerical stability/instability of fast algorithms for solving systems of linear equations or linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. In particular, we consider algorithms which incorporate pivoting without destroying the structure, such as the Gohberg-Kailath-Olshevsky (GKO) algorithm, and describe some recent results on the stability of these algorithms. We also compare these results with the corresponding stability results for algorithms based on the semi-normal equations and for the well known algorithms of Schur/Bareiss and Levinson. TI - Numerical Stability of Some Fast Algorithms for Structured Matrices KW - linear_algebra KW - matrix AU - Brent, Richard ER -