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A variable storage method for conic functions

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Variants of Newton’s method for functions of several variables

Applied Mathematics and Computation, 2006
Newton-like methods are discussed for finding a real solution of a system of nonlinear equations: \(F(x)=0\) in \(\mathbb R^n\). The authors propose a midpoint Newton method: \[ x^{(k+1)} = x^{(k)} - J_F((x^{(k)} + z^{(k)})/2)^{-1}F(x^{(k)}, \quad k=0, 1, \dots. \] Here \(J_F(x)\) is the Jacobian matrix of the function \(F\). \(z^{(k)}\) is defined via
Alicia Cordero, Juan R. Torregrosa
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A method of polynomial interpolation for the functions of several variables

International Journal of Computer Mathematics, 1990
A new algorithm providing polynomial functions of several variables interpolating any values on given points is proposed. The obtained polynomials are more simpler, in degree and number of monomials, than other ones which have appeared in the literature.
F. J. Asencor, Juan-Miguel Gracia
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