QUADRATICALLY CONSTRAINED LEAST-SQUARES AND QUADRATIC PROBLEMS

被引：141

作者：

GOLUB, GH ^{[1
]}

VONMATT, U ^{[1
]}

机构：

[1] SWISS FED INST TECHNOL,INST WISSENSCH RECHNEN,CH-8092 ZURICH,SWITZERLAND

来源：

NUMERISCHE MATHEMATIK | 1991年 / 59卷 / 06期

关键词：

D O I：

10.1007/BF01385796

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following problem: Compute a vector x such that parallel-to Ax - b parallel-to 2 = min, subject to the constraint parallel-to x parallel-to 2 = alpha. A new approach to this problem based on Gauss quadrature is given. The method is especially well suited when the dimensions of A are large and the matrix is sparse. It is also possible to extend this technique to a constrained quadratic form: For a symmetric matrix A we consider the minimization of x(T)Ax - 2b(T)x subject to the constraint parallel-to x parallel-to 2 = alpha. Some numerical examples are given.

引用

页码：561 / 580

页数：20

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