Search

Your search keyword '"López Villellas, Lorién"' showing total 3 results
Start Over Author "López Villellas, Lorién" Topic stagnation
3 results on '"López Villellas, Lorién"'

1. How Accurate Does Newton Have to Be?

Author

Kjelgaard Mikkelsen, Carl Christian, López-Villellas, Lorién, García-Risueño, Pablo, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Deelman, Ewa, editor, and Karczewski, Konrad, editor

Published
2023
Full Text
View/download PDF

2. Newton's method revisited: How accurate do we have to be?

Author

Kjelgaard Mikkelsen, Carl Christian, López‐Villellas, Lorién, and García‐Risueño, Pablo

Subjects
NEWTON-Raphson method, MODULAR arithmetic, SQUARE root, QUASI-Newton methods, MOLECULAR dynamics, NONLINEAR equations
Abstract

Summary: We analyze the convergence of quasi‐Newton methods in exact and finite precision arithmetic using three different techniques. We derive an upper bound for the stagnation level and we show that any sufficiently exact quasi‐Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. In particular, we apply both a symmetric variant and Forsgren's variant of the simplified Newton method. This work has implications for the implementation of quasi‐Newton methods regardless of the scale of the calculation or the machine. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

3. Newton's method revisited : how accurate do we have to be?

Author

Kjelgaard Mikkelsen, Carl Christian, López-Villellas, Lorién, and García-Risueño, Pablo

Subjects
quasi-Newton methods, Computational Mathematics, convergence, approximation error, Beräkningsmatematik, stagnation, rounding error, systems of nonlinear equations
Abstract

We analyze the convergence of quasi-Newton methods in exact and finite precision arithmetic using three different techniques. We derive an upper bound for the stagnation level and we show that any sufficiently exact quasi-Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. In particular, we apply both a symmetric variant and Forsgren's variant of the simplified Newton method. This work has implications for the implementation of quasi-Newton methods regardless of the scale of the calculation or the machine.

Published
2023

Catalog

Books, media, physical & digital resources
See catalog results