Loewner型方程组极小范数最小二乘解的快速算法

Fast Algorithm of Minimal Norm Least Squares Solutionfor Loewnertype Linear System

TONG Qiujuan¹,², LIU Sanyang¹, LU Quan³

1. School of Sciences, Xidian University, Xi’an 710071, China;2. Department of Applied Mathematics and Physics, Xi’an University of Post and Telecommunications, Xi’an 710062, China;3. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China

Received:2007-09-12 Revised:1900-01-01 Online:2008-09-26 Published:2008-09-26
Contact: LIU Sanyang

Abstract

Abstract: A new fast algorithm of the minimal norm least squares solution for the linear system whose coefficient matrix is an m×n Loewnertype matrix with full column rank is given by forming a special block matrix and researching its triangular factorization. Its computation complexity is O(mn)+O(n²), but that of usual algorithms is O(mn²)+O(n³).

Key words: Loewnertype matrix, minimal norm least squares solution, triangular factorization, fast algorithm

CLC Number:

O241.6

TONG Qiujuan,, LIU Sanyang, LU Quan. Fast Algorithm of Minimal Norm Least Squares Solutionfor Loewnertype Linear System[J].J4, 2008, 46(05): 860-864.

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Fast Algorithm of Minimal Norm Least Squares Solutionfor Loewnertype Linear System

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