The QR Decomposition of Toeplitz Matrices

Authors

Adam W. Bojanczyk, Washington University in St. Louis

Document Type

Technical Report

Publication Date

1987-02-01

Filename

WUCS-87-1.pdf

Technical Report Number

WUCS-87-1

Abstract

We present a new algorithm for computing the QR factorization of an mxn Toeplitz matrix in O(mn) multiplications. The algorithm exploits the procedure for the rank-1 modification and the fact that successive columns of a Toeplitz matrix are related to each other. Both matrices Q and R are generated column by column, starting for their first columns. Each column is calculated from the previous column after rank-1 modification to the matrix R and a step of Gramm-Schmidt orthogonalization process applied to two auxiliary vectors.

Comments

Permanent URL: http://dx.doi.org/10.7936/K7R78CJ7

Recommended Citation

Bojanczyk, Adam W., "The QR Decomposition of Toeplitz Matrices" Report Number: WUCS-87-1 (1987). All Computer Science and Engineering Research.
https://openscholarship.wustl.edu/cse_research/794