Results 31 to 40 of about 3,259,619 (178)
Journal of Applied Mathematics, 2013 An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation ∑i=1tMiZiNi=F, where Zi (i=1,2,…,t) are to be determined centro-symmetric matrices with given central principal submatrices.
Li-fang Dai +2 more
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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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Iterative Solution to a System of Matrix Equations
Abstract and Applied Analysis, 2013 An efficient iterative algorithm is presented to solve a system of linear matrix equations , with real matrices and . By this iterative algorithm, the solvability of the system can be determined automatically.
Yong Lin, Qing-Wen Wang
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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
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
wiley +1 more source
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.
openaire +1 more source
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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The Role of Dice in the Emergence of the Probability Calculus
International Statistical Review, Volume 94, Issue 2, Page 464-483, August 2026.Summary The early development of the probability calculus was clearly influenced by the roll of dice. However, while dice have been cast since time immemorial, documented calculations on the frequency of various dice throws date back only to the mid‐13th century.
David R. Bellhouse, Christian Genest
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Floating-Point Roundoff Error Analysis in Artificial Neural Networks
Proceedings of the 25th IMEKO TC4 International Symposium and 23rd International Workshop on ADC and DAC Modelling and Testing, 2022 – In this paper, roundoff errors in Artificial Neural Networks (ANNs) are analyzed on a model for Solid-State Power Amplifiers (SSPAs). Calculations are carried out on 32-bit Floating-Point (FP32) arithmetics, and results are verified using 64-bit floating ...
Hussein Al-Rikabi, B. Renczes
semanticscholar +1 more source
Journal of Computational Chemistry, Volume 47, Issue 20, July 30, 2026.Our GPU software rapidly and accurately computes two‐electron, four‐center Coulomb repulsion integrals using Slater‐type orbitals. It involves applying a simple transformation to eliminate the Coulomb singularity and using the trapezoidal quadrature rule. The quadrature rule converges rapidly, as demonstrated in this graph.
Avleen Kaur +7 more
wiley +1 more source