A modified Shamanskii accelerated scheme via diagonal Jacobian approximation for nonlinear equations - Ibrahim Sulaiman, Mohammed; Mustafa, Mamat (2020)
This paper presents a variation of Newton’s method, based on a diagonal Jacobian approximation scheme on an accelerated Shamanskii process for systems of nonlinear equations especially on problems with singular Fréchet derivative at the solution points. This method aims to reduce the computation cost and storage requirements as in Newton-type methods. Numerical results are presented to illustrate the efficiency of the proposed scheme.