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   Articles with "error bounds" as a keyword



A family of quadrature formulas with their error bounds for convex functions and applications

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recommendations! Published in 2024 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.10460

Abstract: In numerical analysis, the quadrature formulas serve as a pivotal tool for approximating definite integrals. In this paper, we introduce a family of quadrature formulas and analyze their associated error bounds for convex functions. The… read more here.

Keywords: error bounds; quadrature formulas; bounds convex; family quadrature ... See more keywords

Sharp Error Bounds for Weddle's Quadrature via a Novel Twice‐Differentiable Convex Kernel

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recommendations! Published in 2025 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.70283

Abstract: This paper introduces novel error bounds for Weddle's quadrature rule—a sixth‐degree Newton–Cotes numerical integration method—using a new kernel. Unlike classical approaches requiring six‐time differentiability, our results leverage twice‐differentiable convex functions to derive tighter error estimates,… read more here.

Keywords: quadrature; error bounds; weddle quadrature; twice differentiable ... See more keywords
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Fourier–Taylor Approximation of Unstable Manifolds for Compact Maps: Numerical Implementation and Computer-Assisted Error Bounds

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recommendations! Published in 2017 at "Foundations of Computational Mathematics"

DOI: 10.1007/s10208-016-9325-9

Abstract: We develop and implement a semi-numerical method for computing high-order Taylor approximations of unstable manifolds for hyperbolic fixed points of compact infinite-dimensional maps. The method can follow folds in the embedding and describes precisely the… read more here.

Keywords: error bounds; computer assisted; unstable manifolds; taylor approximation ... See more keywords
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Rigorous and effective a-posteriori error bounds for nonlinear problems—application to RB methods

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recommendations! Published in 2020 at "Advances in Computational Mathematics"

DOI: 10.1007/s10444-020-09741-x

Abstract: Quantifying the error that is induced by numerical approximation techniques is an important task in many fields of applied mathematics. Two characteristic properties of error bounds that are desirable are reliability and efficiency. In this… read more here.

Keywords: mathematics; error; error bounds; rigorous effective ... See more keywords

On Long Time Error Bounds for the Wave Equation on Second Order Form

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recommendations! Published in 2018 at "Journal of Scientific Computing"

DOI: 10.1007/s10915-018-0667-0

Abstract: Temporal error bounds for the wave equation expressed on second order form are investigated. We show that, with appropriate choices of boundary conditions, the time and space derivatives of the error are bounded even for… read more here.

Keywords: error; error bounds; second order; bounds wave ... See more keywords

Interpolation Error Bounds for Curvilinear Finite Elements and Their Implications on Adaptive Mesh Refinement

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recommendations! Published in 2019 at "Journal of Scientific Computing"

DOI: 10.1007/s10915-018-0795-6

Abstract: Mesh generation and adaptive refinement are largely driven by the objective of minimizing the bounds on the interpolation error of the solution of the partial differential equation (PDE) being solved. Thus, the characterization and analysis… read more here.

Keywords: error; error bounds; interpolation error; finite elements ... See more keywords

Pointwise Error Bounds in POD Methods Without Difference Quotients

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recommendations! Published in 2024 at "Journal of Scientific Computing"

DOI: 10.1007/s10915-025-02838-9

Abstract: In this paper we consider proper orthogonal decomposition (POD) methods that do not include difference quotients (DQs) of snapshots in the data set. The inclusion of DQs have been shown in the literature to be… read more here.

Keywords: error bounds; dqs; difference quotients; pod methods ... See more keywords

Error Bounds in a Smooth Metric for Brownian Approximation of Dynamical Systems via Stein’s Method

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recommendations! Published in 2025 at "Journal of Statistical Physics"

DOI: 10.1007/s10955-025-03547-1

Abstract: We adapt Stein’s method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric… read more here.

Keywords: dynamical systems; error bounds; stein method; bounds smooth ... See more keywords

Probabilistic error bounds on constraint violation for empirical-analytical Lagrangian models of motion

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recommendations! Published in 2019 at "Nonlinear Dynamics"

DOI: 10.1007/s11071-019-05183-3

Abstract: In contrast to many systems studied in the field of classical mechanics, models of animal motion are often distinguished in that they are both highly uncertain and evolve in a high-dimensional configuration space Q. Often… read more here.

Keywords: probabilistic error; analytical lagrangian; empirical analytical; motion ... See more keywords

New error bounds for linear complementarity problems of S-Nekrasov matrices and B–S-Nekrasov matrices

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recommendations! Published in 2019 at "Computational and Applied Mathematics"

DOI: 10.1007/s40314-019-0818-4

Abstract: In this paper, we give new error bounds for linear complementarity problems when the involved matrices are S-Nekrasov matrices and B–S-Nekrasov matrices, respectively. We prove that the obtained bounds are better than those of Gao… read more here.

Keywords: nekrasov matrices; matrices nekrasov; linear complementarity; new error ... See more keywords

Error Bounds for Identification of a Class of Continuous LTI Systems

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recommendations! Published in 2019 at "IFAC-PapersOnLine"

DOI: 10.1016/j.ifacol.2019.06.098

Abstract: Abstract The main problem in identification of continuous LTI systems is the lack of derivative information of the outputs. If all the derivatives are known exactly, a least squares approach is sufficient to obtain the… read more here.

Keywords: class continuous; lti systems; bounds identification; continuous lti ... See more keywords