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Mixed precision algorithms in numerical linear algebra

, Liang, X. and Schenkels, N. (2020), Exploring variable accuracy storage through lossy compression techniques in numerical linear algebra: A first ...

Accelerating scientific computations with mixed precision algorithms

... x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process ...

Accelerating scientific computations with mixed precision algorithms ...

... x = y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the ...

Fourth-order high-precision algorithms for one-sided tempered ...

Fourth-order high-precision algorithms for one-sided tempered fractional diffusion equations[J]. ... x x 6 , x ∈ ( 0 , 1 ) ,, (5.1). where 1 < α < 2 , and ...

An overview of mixed-precision methods in scientific computing

Mixed precision algorithms in numerical linear algebra. Acta Numerica ... ˆ f(x) = f(x) + εf (x), with |ε0(x)| ≤ ε0, ∀x. d. ∇if(x) = ∇if(x) + εi(x) ...

Arbitrary Precision Algorithms for Computing the Matrix Cosine and ...

Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative ... x \coth(x)$. This method is found to be essentially a variation of ...

Accelerating scientific computations with mixed precision algorithms

... x = y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the ...

Mixed precision algorithms in numerical linear algebra - HAL

converging to a solution x∗. An obvious idea is to use on each iteration arithmetic of the lowest available precision that equals or exceeds the ...

Arbitrary precision algorithms for computing the matrix cosine and its ...

Details on the underlying algorithms can be found in the technical report: A. H. Al-Mohy, N. J. Higham and X. Liu. Arbitrary Precision Algorithms for Computing ...

Precision algorithms in second-order fractional differential equations

Wang, H., & Zheng, X. Analysis and numerical solution of a nonlinear variable-order fractional differential equation. Advances in Computational Mathematics., ...

High-precision algorithms for critical angle refractive index ...

High-precision algorithms for critical angle refractive index measurement. Yun Luo, Wenping Guo, Long Yu, Min Xia, Wei Li ... where x0=xi−w; x2=xi+w; f( ...

DoubleFloats.jl -> Double128 | Quad64? - Page 3 - Julia Discourse

... precision algorithms are used (BigFloat, ArbNumerics). It is ... using what I had called ulp(x) or, equivalently my eps(x)/2 : ... w ...

Advances in Mixed Precision Algorithms: 2021 Edition - OSTI.GOV

; Li, X.; Lindquist, N.; Liu, Y.; Loe, J.

Accelerating scientific computations with mixed precision algorithms

Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve ...