scholarly journals The minimum-norm least-squares solution of a linear system and symmetric rank-one updates

2011 ◽  
Vol 22 ◽  
Author(s):  
Xuzhou Chen ◽  
Jun Ji
Keyword(s):  
Linear System ◽  
Least Squares ◽  
Minimum Norm ◽  
Least Squares Solution ◽  
Rank One ◽  
Symmetric Rank One

A Least-Squares Solution of a Linear System

SIAM Review ◽  
1962 ◽  
Vol 4 (2) ◽  
pp. 150-150
Author(s):  
Franklin W. Diederich
Keyword(s):  
Linear System ◽  
Least Squares ◽  
Least Squares Solution

A Least-Squares Solution of a Linear System (Franklin W. Dtederich)

SIAM Review ◽  
1964 ◽  
Vol 6 (2) ◽  
pp. 182-183
Author(s):  
Victor Chew ◽  
M. J. Synge
Keyword(s):  
Linear System ◽  
Least Squares ◽  
Least Squares Solution

The Minimum Norm Least-Squares Solution in Reduction by Krylov Subspace Methods

2016 ◽  
Vol 26 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Xinsheng Wang ◽  
Chenxu Wang ◽  
Mingyan Yu
Keyword(s):  
Least Squares ◽  
Computer Aided Design ◽  
Large Scale ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Small Scale ◽  
Minimum Norm ◽  
Subspace Projection ◽  
Subspace Methods ◽  
Least Squares Solution

In recent years, model order reduction (MOR) of interconnect system has become an important technique to reduce the computation complexity and improve the verification efficiency in the nanometer VLSI design. The Krylov subspaces techniques in existing MOR methods are efficient, and have become the methods of choice for generating small-scale macro-models of the large-scale multi-port RCL networks that arise in VLSI interconnect analysis. Although the Krylov subspace projection-based MOR methods have been widely studied over the past decade in the electrical computer-aided design community, all of them do not provide a best optimal solution in a given order. In this paper, a minimum norm least-squares solution for MOR by Krylov subspace methods is proposed. The method is based on generalized inverse (or pseudo-inverse) theory. This enables a new criterion for MOR-based Krylov subspace projection methods. Two numerical examples are used to test the PRIMA method based on the method proposed in this paper as a standard model.

scholarly journals Perturbation bounds for the Moore-Penrose inverse of operators

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 353-362
Author(s):  
Xiaoji Liu ◽  
Yonghui Qin ◽  
Dragana Cvetkovic-Ilic
Keyword(s):  
Hilbert Space ◽  
Least Squares ◽  
Minimum Norm ◽  
Perturbation Bounds ◽  
Least Squares Solution ◽  
Relative Errors

We consider the perturbation bounds for the Moore-Penrose inverse of a given operator on Hilbert space and apply these results to the relative errors of the minimum norm least squares solution of the equation Ax = b.

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