Results 31 to 40 of about 67,589 (200)
Numerical Integration in Arbitrary-Precision Ball Arithmetic [PDF]
, 2018 We present an implementation of arbitrary-precision numerical integration with rigorous error bounds in the Arb library. Rapid convergence is ensured for piecewise complex analytic integrals by use of the Petras algorithm, which combines adaptive bisection with adaptive Gaussian quadrature where error bounds are determined via complex magnitudes ...
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Semantics, Specification Logic, and Hoare Logic of Exact Real Computation [PDF]
Logical Methods in Computer ScienceWe propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the algorithmic ...
Sewon Park +9 more
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Computing Puiseux series : a fast divide and conquer algorithm [PDF]
, 2017 Let $F\in \mathbb{K}[X, Y ]$ be a polynomial of total degree $D$ defined over a perfect field $\mathbb{K}$ of characteristic zero or greater than $D$. Assuming $F$ separable with respect to $Y$ , we provide an algorithm that computes the singular parts ...
Poteaux, Adrien, Weimann, Martin
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Improving MATLAB's isprime performance without arbitrary-precision arithmetic
CoRR, 2021 MATLAB is a numerical computing platform used by scientists, engineers, mathematicians, and students which contains many mathematical functions, including isprime. MATLAB's isprime function determines which elements of an input array are prime. This research details modular arithmetic techniques, the Miller-Rabin primality test, vectorized operations ...
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Certified lattice reduction [PDF]
, 2019 Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been improved in many
Espitau, Thomas, Joux, Antoine
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IEEE Access, 2019 Geometric algorithms rely on predicates, among them, the 2D and 3D orientation and incircle tests are important ones. Shewchuk's adaptive floating-point predicate is a well-known C implementation, which is embedded in many computational geometry ...
Meng Qi, Ke Yan, Yuanjie Zheng
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Electric potential and field calculation of charged BEM triangles and rectangles by Gaussian cubature [PDF]
, 2016 It is a widely held view that analytical integration is more accurate than the numerical one. In some special cases, however, numerical integration can be more advantageous than analytical integration.
Glück, Ferenc, Hilk, Daniel
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Software Support for Arbitrary Precision Arithmetic in Programming Languages
Indian Journal of Cryptography and Network Security, 2023 Arbitrary precision arithmetic, also known as bignum arithmetic, is a computational technique that allows programmers to perform arithmetic operations on numbers with significantly higher precision and magnitude than what is typically supported by the built-in numerical data types in programming languages.
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Cartographic Algorithms: Problems of Implementation and Evaluation and the Impact of Digitising Errors [PDF]
, 1991 Cartographic generalisation remains one of the outstanding challenges in digital cartography and Geographical Information Systems (GIS). It is generally assumed that computerisation will lead to the removal of spurious variability introduced by the ...
Visvalingam, M. +2 more
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Applied Sciences, 2018 In high-throughput applications, low-complexity and low-latency channel decoders are inevitable. Hence, for low-density parity-check (LDPC) codes, message passing decoding has to be implemented with coarse quantization—that is, the exchanged ...
Maximilian Stark +2 more
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