The concept of best vector used to solve ill-posed linear inverse problems
Resource
Computer Modeling in Engineering & Sciences, 83(5), 499-525
Journal
Computer Modeling in Engineering & Sciences
Journal Volume
83
Journal Issue
5
Pages
499-525
Date Issued
2012
Date
2012
Author(s)
Liu, Chein-Shan
Abstract
The iterative algorithms based on the concept of best vector are pro- posed to solve an ill-conditioned linear system: Bx b = 0, which might be a discretization of linear inverse problem. In terms of r := Bx b and a monotoni- cally increasing positive function Q(t) of a time-like variable t, we define a future cone in the Minkowski space, wherein the discrete dynamics of the proposed algo- rithm is evolved. We propose two methods to approximate the best vector B 1 r, and obtain three iterative algorithms for solving x, which we label them as the steepest-descent and optimal vectors iterative algorithm (SOVIA), the mixed opti- mal iterative algorithm (MOIA), as well as the optimal vector iterative algorithm (OVIA). These algorithms are compared with the relaxed steepest descent method (RSDM), the conjugate gradient method (CGM) and an optimal iterative algorithm with an optimal descent vector (OIA/ODV) by testing several ill-posed linear in- verse problems.
Type
journal article
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