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How Accurate is Richardson's Error Estimate?

Concurrency and Computation: Practice and Experience, Volume 37, Issue 27-28, 25 December 2025.
ABSTRACT We consider the fundamental problem of estimating the difference between the exact value T$$ T $$ and approximations Ah$$ {A}_h $$ that depend on a single real parameter h$$ h $$. It is well‐known that if the error Eh=T−Ah$$ {E}_h=T-{A}_h $$ satisfies an asymptotic expansion, then we can use Richardson extrapolation to approximate Eh$$ {E}_h $$
Carl Christian Kjelgaard Mikkelsen, Lorién López‐Villellas   +1 more
wiley   +1 more source

Symplectic integration without roundoff error [PDF]

, 2006
Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious damping or excitation.
openaire   +2 more sources

Solving the Net Worth Optimization Problem

FINANCIAL PLANNING REVIEW, Volume 8, Issue 4, December 2025.
ABSTRACT The mean–variance optimization (MVO) model of Harry M. Markowitz is the foundation of quantitative portfolio construction and asset allocation. While Markowitz originally developed MVO for forming portfolios of tradable assets in isolation, it has been adapted for creating portfolios of tradable assets in the presence of non‐tradable assets ...
Paul D. Kaplan
wiley   +1 more source

Simple but accurate periodic solutions for the nonlinear pendulum equation

Revista Brasileira de Ensino de Física
Despite its elementary structure, the simple pendulum oscillations are described by a nonlinear differential equation whose exact solution for the angular displacement from vertical as a function of time cannot be expressed in terms of an elementary ...
Fábio M.S. Lima
doaj   +1 more source

Certified Roundoff Error Bounds Using Semidefinite Programming [PDF]

ACM Transactions on Mathematical Software, 2017
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance, for FPGAs or custom hardware implementations.
Victor Magron, George A. Constantinides, Alastair F. Donaldson   +2 more
openaire   +4 more sources

Mixed Precision Iterative Refinement for Least Squares With Linear Equality Constraints and Generalized Least Squares Problems

Numerical Linear Algebra with Applications, Volume 32, Issue 5, October 2025.
ABSTRACT Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which is the solver for the least squares problem. By transforming least squares problems into augmented linear systems, mixed precision techniques are capable of refining the lower precision solution to the working ...
Bowen Gao, Yuxin Ma, Meiyue Shao
wiley   +1 more source

USING RATIONAL NUMBERS AND PARALLEL COMPUTING TO EFFICIENTLY AVOID ROUND-OFF ERRORS ON MAP SIMPLIFICATION

Revista Brasileira de Cartografia, 2018
This paper presents EPLSimp, an algorithm for map generalization that avoids the creation of topological inconsistencies. EPLSimp is based on Visvalingam-Whyatt's (VW) algorithm on which least "important" points are removed first.
Maurício G. Gruppi, Salles V. G. de Magalhães, Marcus V. A. Andrade, W. Randolph Franklin, Wenli Li   +4 more
doaj  

On Stochastic Roundoff Errors in Gradient Descent with Low-Precision Computation

Journal of Optimization Theory and Applications, 2023
Lu Xia, Stefano Massei, M. Hochstenbach, B. Koren   +3 more
semanticscholar   +1 more source

tmm4py: Global Ocean Biogeochemical Modeling in Python With the Transport Matrix Method

Journal of Advances in Modeling Earth Systems, Volume 17, Issue 8, August 2025.
Abstract Marine biogeochemical models are important tools in the quest to understand the cycling of chemical and biological tracers such as nutrients, carbon and oxygen, as well as key components of the Earth System Models used to project climate change.
Samar Khatiwala
wiley   +1 more source

A Review of Green's Function Methods for Tracer Timescales and Pathways in Ocean Models

Journal of Advances in Modeling Earth Systems, Volume 17, Issue 7, July 2025.
Abstract Understanding advective‐diffusive dispersal of trace substances in environmental fluids like the global ocean is a ubiquitous challenge in geophysics. Since the turn of the millennium, substantial progress has been made in the theory, implementation in models, and application of such tracers in oceanography.
Thomas W. N. Haine, Stephen M. Griffies, Geoffrey Gebbie, Wenrui Jiang   +3 more
wiley   +1 more source