Square-root free orthogonalization algorithms

Author

Hasan, Mohammed A.

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Duluth, MN

fYear

2009

fDate

19-24 April 2009

Firstpage

3173

Lastpage

3176

Abstract

This paper is concerned with the derivation and analysis of higher order algorithms of polynomial type for computing an orthonormal basis of a subspace. These algorithms are derived from unconstrained optimization of certain cost functions. The proposed methods are efficient and do not require square root computation. Based on these, algorithms for orthonormalization with respect to a positive definite matrix and principal and minor subspace methods are developed. Numerical experiments illustrate the theoretical results.

Keywords

optimisation; polynomials; certain cost function; orthonormal basis; positive definite matrix; square root computation; square root free orthogonalization; unconstrained optimization; Algorithm design and analysis; Computer applications; Cost function; Equations; Independent component analysis; Least squares methods; Lyapunov method; Matrix decomposition; Polynomials; Stability; Gram-Schmidt Process; Orthonormalization; global stability; higher order fixed point polynomials;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on

Conference_Location

Taipei

ISSN

1520-6149

Print_ISBN

978-1-4244-2353-8

Electronic_ISBN

1520-6149

Type

conf

DOI

10.1109/ICASSP.2009.4960298

Filename

4960298