Eigenvalue decomposition-based modified Newton algorithm. (English) Zbl 1299.65104

Summary: When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.


65H10 Numerical computation of solutions to systems of equations
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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