ISSN:
1572-9265
Keywords:
Cholesky factorization error analysis
;
Hankel matrix
;
least squares
;
normal equations
;
orthogonal factorization
;
QR factorization
;
semi-normal equations
;
stability
;
Toeplitz matrix
;
weak stability
;
Primary 65F25
;
Secondary 47B35
;
65F05
;
65F30
;
65Y05
;
65Y10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We show that a fast algorithm for theQR factorization of a Toeplitz or Hankel matrixA is weakly stable in the sense thatR T R is close toA T A. Thus, when the algorithm is used to solve the semi-normal equationsR TRx=AT b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear systemAx=b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem min ||Ax-b||2.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02140770
