DISPLACEMENT STRUCTURE - THEORY AND APPLICATIONS

被引：290

作者：

KAILATH, T ^{[1
]}

SAYED, AH ^{[1
]}

机构：

[1] UNIV CALIF SANTA BARBARA, DEPT ELECT & COMP ENGN, SANTA BARBARA, CA 93106 USA

来源：

SIAM REVIEW | 1995年 / 37卷 / 03期

关键词：

DISPLACEMENT STRUCTURE; STRUCTURED MATRICES; GENERALIZED SCHUR ALGORITHM; TRIANGULAR MATRIX FACTORIZATION; INTERPOLATION THEORY; TIME-VARIANT STRUCTURES; STATE-SPACE MODELS; KALMAN FILTERING; ADAPTIVE FILTERING;

D O I：

10.1137/1037082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this survey paper, we describe how strands of work that are important in two different fields, matrix theory and complex function theory, have come together in some work on fast computational algorithms ibr matrices with what we call displacement structure. In particular, a fast triangularization procedure can be developed for such matrices, generalizing in a striking way an algorithm presented by Schur(1917) [J. Reine Angew. Math., 147 (1917), pp. 205-232] in a paper on checking when a power series is bounded in the unit disc. This factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra. We mention, among others inverse scattering, analytic and unconstrained rational interpolation theory, digital filter design, adaptive filtering, and state-space least-squares estimation.

引用

页码：297 / 386

页数：90

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