Solving Separable Nonlinear Equations Using LU Factorization | Zendy

Yun-Qiu Shen | Zendy; Tjalling Ypma | Zendy

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Solving Separable Nonlinear Equations Using LU Factorization

Author(s) -

Yun-Qiu Shen,

Tjalling Ypma

Publication year - 2013

Publication title -

isrn mathematical analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-4665

pISSN - 2090-4657

DOI - 10.1155/2013/258072

Subject(s) - overdetermined system , system of linear equations , mathematics , nonlinear system , factorization , rank (graph theory) , separable space , matrix (chemical analysis) , differentiable function , mathematical analysis , algorithm , physics , materials science , quantum mechanics , combinatorics , composite material

Separable nonlinear equations have the form where the matrix and the vector are continuously differentiable functions of and . We assume that and has full rank. We present a numerical method to compute the solution for fully determined systems () and compatible overdetermined systems (). Our method reduces the original system to a smaller system of equations in alone. The iterative process to solve the smaller system only requires the LU factorization of one matrix per step, and the convergence is quadratic. Once has been obtained, is computed by direct solution of a linear system. Details of the numerical implementation are provided and several examples are presented.

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