Toeplitz Matrices: Algebra and Algorithms
Abstract
In this research project, we analyze the mathematical structure and numerical algorithms associated with Toeplitz matrices. Toeplitz matrices arise in a number of problems in engineering and applied mathematics. In many such problems, the task is to solve for certain parameters of interest (such as predictor polynomial, reflection coefficients, and solution to a linear system) in a computationally efficient manner. Also, the numerical stability aspects of the various algorithms must be examined from the standpoint of implementation using finite precision arithmetic. We have derived fast (order-recursive) and superfast (fast Fourier transform based) algorithms for solving a Toeplitz linear system. The algorithms reported here are some of the most computationally efficient algorithms. Also, the numerical stability of the split Levinson algorithm is examined and it is established that it is weakly stable. Furthermore the various classical and split Levinson algorithms are studied for the effects of finite precision arithmetic. An interesting relationship between Levinson algorithm and stability tests for discrete systems is exploited to derive a new computationally efficient algorithm for testing the wide sense stability of discrete time systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 31, 1990
- Accession Number
- ADA223174
Entities
People
- Hari Krishna
Organizations
- Syracuse University