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- W2080573284 abstract "We propose an algorithm for implementing Newton’s method for a general nonlinear system $f(x) = 0$ where the linear systems that arise at each step of Newton’s method are solved by a preconditioned Krylov subspace iterative method. The algorithm requires only function evaluations and does not require the evaluation or storage of the Jacobian matrix. Matrix-vector products involving the Jacobian matrix are approximated by directional differences. We develop a framework for constructing preconditionings for this inner iterative method which do not reference the Jacobian matrix explicitly. We derive a nonlinear SSOR type preconditioning which numerical experiments show to be as effective as the linear SSOR preconditioning that uses the Jacobian explicitly." @default.
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- W2080573284 date "1984-09-01" @default.
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- W2080573284 title "Nonlinearly Preconditioned Krylov Subspace Methods for Discrete Newton Algorithms" @default.
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- W2080573284 doi "https://doi.org/10.1137/0905039" @default.
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