On fully discrete collocation methods for solving weakly singular integral equations
Mathematical Modelling and Analysis, 2009 A popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be ...
Raul Kangro, Inga Kangro
doaj +1 more source
Solution of Dense Linear Systems via Roundoff-Error-Free Factorization Algorithms
ACM Transactions on Mathematical Software, 2018 Exact solving of systems of linear equations (SLEs) is a fundamental subroutine within number theory, formal verification of mathematical proofs, and exact-precision mathematical programming.
Adolfo R. Escobedo +2 more
semanticscholar +1 more source
Optimal Controller and Filter Realisations using Finite-precision, Floating- point Arithmetic. [PDF]
, 2005 The problem of reducing the fragility of digital controllers and filters implemented using finite-precision, floating-point arithmetic is considered.
Chen, Sheng +3 more
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Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations [PDF]
, 2015 We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which is motivated by a particular singularity formation scenario observed in numerical computation.
Hou, Thomas Y., Liu, Pengfei
core +5 more sources
Quantization in Control Systems and Forward Error Analysis of Iterative Numerical Algorithms [PDF]
, 2010 The use of control theory to study iterative algorithms, which can be considered as dynamical systems, opens many opportunities to find new tools for analysis of algorithms.
Constantinides, GA +2 more
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Round-Off Error Suppression by Statistical Averaging
AxiomsRegarding round-off errors as random is often a necessary simplification to describe their behavior. Assuming, in addition, the symmetry of their distributions, we show that one can, in unstable (ill-conditioned) computer calculations, suppress their ...
Andrej Liptaj
doaj +1 more source
A Model for Understanding Numerical Stability
, 2005 We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore capable of ...
Bornemann, Folkmar
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Automated Roundoff Error Analysis of Probabilistic Floating-Point Computations
ACM Transactions on Probabilistic Machine LearningWe present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are generally ...
George A. Constantinides +3 more
semanticscholar +1 more source
A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4
, 2018 Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing.
Becker, Heiko +5 more
core +1 more source
Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity [PDF]
, 2007 The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for ...
Harald P. Pfeiffer +6 more
core +2 more sources