Solution of the Yule-Walker equations

I. Gohberg; Israel Koltracht; Tongsan D. Xiao

doi:10.1117/12.49808

1 December 1991 Solution of the Yule-Walker equations

I. Gohberg, Israel Koltracht, Tongsan D. Xiao

Proceedings Volume 1566, Advanced Signal Processing Algorithms, Architectures, and Implementations II; (1991) https://doi.org/10.1117/12.49808
Event: San Diego, '91, 1991, San Diego, CA, United States

Abstract

The structured condition number of the solution of the Yule-Walker system of equations is given. It is found that there is little difference between this structured condition and the general condition number of a Toeplitz matrix. As a consequence, general purpose linear system solvers are stable for solving the Yule-Walker equations. By constructing appropriate examples it is shown that the Levinson algorithm is only weakly stable and is less trustworthy than the LDL^T algorithm. Our round-off error analysis also suggests that for better accuracy Schur coefficients should be computed by the Schur algorithm and then used in the Levinson algorithm for computing the solution of Yule-Walker equations.

Citation Download Citation

I. Gohberg, Israel Koltracht, and Tongsan D. Xiao "Solution of the Yule-Walker equations", Proc. SPIE 1566, Advanced Signal Processing Algorithms, Architectures, and Implementations II, (1 December 1991); https://doi.org/10.1117/12.49808

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available