99 citations · 459 across the 24 of their papers we have counts for
25 papers
Improving the accuracy of the fast inverse square root algorithm
Cezary J. Walczyk, Leonid V. Moroz, Jan L. Cieśliński
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fa…
Fast calculation of inverse square root with the use of magic constant analytical approach
Leonid V. Moroz, Cezary J. Walczyk, Andriy Hrynchyshyn +2
We present a mathematical analysis of transformations used in fast calculation of inverse square root for single-precision floating-point numbers. Optimal values of the so called m…
Improving the accuracy of the AVF method
Jan L. Cieśliński
The Average Vector Field (AVF) method is a B-series scheme of the second order. As a discrete gradient method it preserves exactly the energy integral for any canonical Hamiltonian…
Locally exact modifications of discrete gradient schemes
Jan L. Cieśliński
Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidi…
Locally exact modifications of numerical schemes
Jan L. Cieśliński
We present a new class of exponential integrators for ordinary differential equations: locally exact modifications of known numerical schemes. Local exactness means that they prese…
Locally exact modifications of numerical integrators
Jan L. Cieśliński
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every…