1999/01/01 by Richard P. Brent · 1 citation
Computer Science · Mathematics · #Matrix Theory and Algorithms #Mathematical functions and polynomials #Advanced Optimization Algorithms Research #Toeplitz matrix #Stability (learning theory) #Rank (graph theory) #Algorithm #Linear system #Mathematics #Displacement (psychology) #Computer science #Applied mathematics #Mathematical analysis #Pure mathematics #Combinatorics
paper · doi:10.1137/1.9781611971354.ch4
openalex publication_date 1999/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We survey the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. We consider algorithms which incorporate pivoting without destroying the structure, and describe some recent results on the stability of these algorithms. We also compare these results with the corresponding stability results for the well known algorithms of Schur/Bareiss and Levinson, and for algorithms based on the semi-normal equations.