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    A Scalar Homotopy Method for Solving an Over/Under-Determined System of Non-Linear Algebraic Equations

    Chein-Shan Liu1, Weichung Yeih2, Chung-Lun Kuo3, Satya N. Atluri4

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 47-72, 2009, DOI:10.3970/cmes.2009.053.047

    Abstract Iterative algorithms for solving a system of nonlinear algebraic equations (NAEs): Fi(xj) = 0, i, j = 1,... ,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm is still the most popular one to solve the NAEs, due to the ease of its numerical implementation. However, this type of algorithm is sensitive to the initial guess of solution, and is expensive in terms of the computations of the Jacobian matrix ∂Fi/∂xj and its inverse at each iterative step. In addition, the Newton-like methods restrict one to construct an iteration procedure for n-variables… More >

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