A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that RT R is close to AT A. Thus, when the algorithm is used to solve the semi-normal equations RT Rx = AT b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithmalso applies to the solution of the full-rank Toeplitz or Hankel least squares problem minkAx, bk2. 1991 Mathematics Subject Classi cation. Primary 65F25; Secondary 47B35, 65F05, 65F30, 65Y05, 65Y10 Key words and phrases. Cholesky factorization, error analysis, Hankel matrix, least squares, normal equations, orthogonal factorization, QR factorization, semi-normal equations, stability, Toeplitz matrix, weak stability.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Adam W. Bojanczyk, Richard P. Brent, Frank R. de Hoog
• Keywords: CORR 2010, Education, Hankel Matrix, QR Factorization, Semi-normal Equations