Algorithm for generating orthogonal matrices with rational elements
Ruslan Sharipov
Abstract
Special orthogonal matrices with rational elements form the group SO(n,Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for generating such matrices by means of random number routines.
Create a lesson
Related papers
The Art of Closed-Formula Defaults: Search-Free Code Generation for Tensor Operators
Paolo D'Alberto, Ashish Sirasao
Geometric Function Atlas: certified computing for geometric function theory in Python
Kishan Gurumurthy, Pushparaj Devadiga, Prasanna Devadiga et al.
Gradient Reconstruction in Lattice Boltzmann Methods for Systems of Conservation Laws
Adrian Kummerländer, Fedor Bukreev, Mathias J. Krause
BF16 Component-Product Emulation of FP32 and FP64 GEMM on Intel AMX
Bing Cui, Yu Liu
GRADSOLVE: fast exact gradients for ODE ensembles on GPUs
Alessio Spurio Mancini
Performance Evaluation of Fast Fourier Transforms on Emerging RISC-V Hardware with Vector Extension Support
Daniel Seibel, Kaveh Haghighi Mood, Jayesh Badwaik et al.