Results 11 to 20 of about 337 (147)
An Introduction to Affine Arithmetic
Trends in Computational and Applied Mathematics, 2003 Affine arithmetic (AA) is a model for self-validated computation which, like standard interval arithmetic (IA), produces guaranteed enclosures for computed quantities, taking into account any uncertainties in the input data as well as all internal ...
J. Stolfi, L.H. de Figueiredo
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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
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Nonconcurrent Error Correction in the Presence of Roundoff Noise [PDF]
Proceedings of the 45th IEEE Conference on Decision and Control, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Takos, G. +3 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
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Cycles and circles in roundoff errors
Physical Review E, 1993 CYCLER Paper 93feb007 ascii with figures available from ...
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Stochastic Estimation of MIMO Detection Error Caused by Low-Bitwidth QR Decomposition
IEEE Open Journal of the Communications SocietyIn this paper, we propose a new approach to justify a roundoff error impact on the accuracy of the linear least squares (LS) solution using QR decomposition.
Alexander Osinsky +4 more
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On numerical stability of continued fractions
Математичні СтудіїThe paper considers the numerical stability of the backward recurrence algorithm (BR-algorithm) for computing approximants of the continued fraction with complex elements.
V. Hladun +3 more
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Register‐Efficient Linear‐Time Evaluation in the Bernstein Basis
Computer Graphics Forum, EarlyView.Abstract We investigate the evaluation of points and derivatives of Bézier curves and surfaces on modern architectures, focusing on performance and guided by numerical error bounds. While the de Casteljau algorithm remains the reference for numerical robustness, its linear working‐set size imposes substantial register pressure on GPUs.
Gábor Valasek, Anna Lili Horváth
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A stochastic roundoff error analysis for the convolution [PDF]
Mathematics of Computation, 1992 We study the accuracy of an algorithm which computes the convolution via Radix-2 fast Fourier transforms. Upper bounds are derived for the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication.
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Bidiagonal Decompositions and High‐Accuracy Computations for Newton Collocation Matrices
Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.ABSTRACT We consider a class of collocation matrices A$$ A $$ associated with the Newton basis of the space of polynomials of degree at most n$$ n $$, evaluated at a set of l+1≥n+1$$ l+1\ge n+1 $$ nodes. In the most general setting, we allow n$$ n $$ of these nodes to either coincide with or differ from those defining the Newton basis.
E. Mainar, A. Marco, B. Rubio, R. Viaña
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