THE QR ALGORITHM FOR UNITARY HESSENBERG MATRICES

作     者：GRAGG, WB 

作者机构：UNIV KENTUCKYDEPT MATHLEXINGTONKY 40506 

出 版 物：《JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS》 (计算与应用数学杂志)

年 卷 期：1986年第16卷第1期

页      面：1-8页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation, NSF, (DMS-8404980) Australian National University, ANU 

主　　题：QR algorithm Szegö polynomials Gauss-Szegö quadrature 

摘      要：Let H be an n × n unitary right Hessenberg matrix with positive subdiagonal elements. Using what we call the Schur parameterization of H , we show how one step of the shifted QR algorithm for H can be carried out in O( n ) arithmetic operations. Coupled with the shift strategy of Eberlein and Huang [3], this will permit computation of the spectrum of H , to machine precision, in O( n 2 ) operations. One potential application is the computation of Gauss-Szegö quadrature formulas [12], given the associated Schur parameters [7]. The weights can also be computed, by direct analogy with [6].