The Globally Optimal Iterative Algorithm with Critical Vector as a Descent Direction to Solve Algebraic Equations
Date Issued
2012
Date
2012
Author(s)
Hsu, Chia-Jou
Abstract
It has always been of interest to solve algebraic equations used for describing physical and engineering issues. By using the concepts of the Steepest Descent method, the scalar homotopy method and the structure of light cone, we have developed a novel algorithm with preset parameters ϒ(0≤ϒ<1),ac (ac>1) and the critical parameter αc in the driving vector u=R+αcr and u=BTF+αcF as a descent direction. Due to the criticality of αc, we believe that by using this algorithm, the globally optimal solution can be obtained. It is so call the Globally Optimal Iterative Algorithm (GOIA).
The GOIA has performed both great efficiency and accuracy when it is used for solving algebraic equations. Moreover, by using the GOIA, one can successfully avoid the calculation of the inverse Jacobian matrix which is required when use the Newton’s method instead.
The GOIA has performed both great efficiency and accuracy when it is used for solving algebraic equations. Moreover, by using the GOIA, one can successfully avoid the calculation of the inverse Jacobian matrix which is required when use the Newton’s method instead.
Subjects
algebraic equations
Steepest Descent method
scalar homotopy method
light cone
Globally Optimal Iterative Algorithm (GOIA)
Newton’s method
Type
thesis
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