Generalized linearization of nonlinear algebraic equations: an innovative approach

Details Generalized linearization of nonlinear algebraic equations: an innovative approach Generalized linearization of nonlinear algebraic equations: an innovative approach

1999-05-07

arxiv.org/abs/math/9905042v2

Mathematics

Numerical Analysis

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Scientific paper

Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear system. In this way, all nonlinear algebraic terms are instead expressed as Linearly independent variables. Therefore, a n-dimension nonlinear system can be expanded as a linear system of n(n+1)/2 dimension space. This introduces the possibility to applying generalized inverse of matrix to computation of nonlinear systems. Also, singular value decomposition (SVD) can be directly employed in nonlinear analysis by using such a methodology.

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