Abstract/Details

## Numerical analysis of mappings associated with positive definite Toeplitz matrices

Xiao, Ding.   University of Connecticut ProQuest Dissertations Publishing,  1992. 9310257.

### Abstract (summary)

Associated with an $(n+1)\times(n+1)$ positive definite Toeplitz matrix $A=\{a\sb{\vert i-j\vert}\}\sbsp{i,j=0}{n}$, there are three groups of parameters, which are called reflection coefficients, autocorrelation sequence and AR parameters. They appear in a wide variety of applications in science and engineering such as theory of analytic functions, geophysics, speech processing, statistics, transmission lines and others. These three sets of parameters are in one to one correspondence with each other. In this dissertation, the numerical behavior of the maps from autocorrelation sequence to reflection coefficients, from autocorrelation sequence to AR parameters and from reflection coefficients to autocorrelation sequence are studied. The error analysis of Levinson algorithm, Schur algorithm and Direct algorithm for computing these maps is given. It is found that Schur and Levinson algorithms are forward stable to compute both the AR parameters and reflection coefficients. We also show that Direct algorithm is a stable algorithm for computing autocorrelation sequence. The formulas and efficient algorithms for the condition numbers of these three maps are given.

### Indexing (details)

Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; AR parameters; autocorrelation; reflection coefficients
Title
Numerical analysis of mappings associated with positive definite Toeplitz matrices
Author
Xiao, Ding
Number of pages
84
Degree date
1992
School code
0056
Source
DAI-B 53/12, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-208-01292-5
Advisor
Koltracht, I.
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9310257
ProQuest document ID
303994475
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303994475/abstract