Fourier–Taylor Approximation of Unstable Manifolds for Compact Maps: Numerical Implementation and Computer-Assisted Error Bounds
Sign Up to like & getrecommendations! 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
Rigorous and effective a-posteriori error bounds for nonlinear problems—application to RB methods
Sign Up to like & getrecommendations! 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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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
Sign Up to like & getrecommendations! 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
Probabilistic error bounds on constraint violation for empirical-analytical Lagrangian models of motion
Sign Up to like & getrecommendations! 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
Sign Up to like & getrecommendations! 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
Sign Up to like & getrecommendations! 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
Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces
Sign Up to like & getrecommendations! Published in 2022 at "Stochastic Processes and their Applications"
DOI: 10.1016/j.spa.2022.03.009
Abstract: We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the first time, we include in this study the analysis of non-zero initial conditions.… read more here.
Keywords: error bounds; feedback controlled; bounds model; model reduction ... See more keywords
Error bounds for the perturbation solution of the transition density under a multi-factor CIR term structure model with weak mean-reversion effect
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Statistics - Theory and Methods"
DOI: 10.1080/03610926.2019.1617879
Abstract: Abstract We consider a multi-factor Cox-Ingersoll-Ross (CIR) model of the term structure of interest rates with weak mean-reversion effect. We use perturbation theory to analyze its conditional characteristic function illustrated by a system of Riccati… read more here.
Keywords: error bounds; term structure; multi factor; transition density ... See more keywords
Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations
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DOI: 10.1103/physreva.101.052122
Abstract: In arXiv:2001.03419 we introduce a universal error bound for constrained unitary dynamics within a well-gapped energy band of an isolated quantum system. Here, we provide the full details on the derivation of the bound. In… read more here.
Keywords: bounds constrained; constrained dynamics; dynamics gapped; quantum systems ... See more keywords
Error Bounds for Localization in mmWave MIMO Systems: Effects of Hardware Impairments Considering Perfect and Imperfect Clock Synchronization
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Systems Journal"
DOI: 10.1109/jsyst.2022.3163021
Abstract: Localization demands high-accuracy positioning, and this rings especially true in the context of fifth-generation (5G) millimeter-wave (mmWave) systems. However, it is easier said than done. mmWave systems require a large number of antennas to be… read more here.
Keywords: localization; synchronization; error bounds; clock synchronization ... See more keywords