Recursive Vectorized Computation of the Vector p -norm
Abstract
Recursive algorithms for computing the Frobenius norm of a real array are proposed, based on [Formula: see text], a hypotenuse function. Comparing their relative accuracy bounds with those of the BLAS routine [Formula: see text] it is shown that the proposed algorithms could in many cases be significantly more accurate. The scalar recursive algorithms are vectorized with the Intel’s vector instructions to achieve performance comparable to [Formula: see text], and are further parallelized with OpenCilk. Some scalar algorithms are unconditionally bitwise reproducible, while the reproducibility of the vector ones depends on the vector width. A modification of the proposed algorithms to compute the vector [Formula: see text]-norm is also presented.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Tensor decomposition and applications
Polynomial and algebraic computation
Publication details
- Journal / source
- Parallel Processing Letters
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 36
- Issue
- 01n02
- Publication date
- 12 February 2026
- Language
- EN