Sökning: L773:1532 0626 OR L773:1532 0634 >
Newton's method rev...
Newton's method revisited : how accurate do we have to be?
-
- Kjelgaard Mikkelsen, Carl Christian, 1976- (författare)
- Umeå universitet,Institutionen för datavetenskap
-
- López-Villellas, Lorién (författare)
- Barcelona Supercomputing Center, Barcelona, Spain
-
- García-Risueño, Pablo (författare)
- Independent Scholar, Berlin, Germany
-
(creator_code:org_t)
- John Wiley & Sons, 2024
- 2024
- Engelska.
-
Ingår i: Concurrency and Computation. - : John Wiley & Sons. - 1532-0626 .- 1532-0634. ; 36:10
- Relaterad länk:
-
https://doi.org/10.1...
-
visa fler...
-
https://umu.diva-por... (primary) (Raw object)
-
https://urn.kb.se/re...
-
https://doi.org/10.1...
-
visa färre...
Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- approximation error
- convergence
- quasi-Newton methods
- rounding error
- stagnation
- systems of nonlinear equations
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
Hitta via bibliotek
Till lärosätets databas