The advent of transformers has brought about significant advancements in traditional
machine learning tasks. However, their pervasive deployment has raised concerns about …

We present a model for computation over the reals or an arbitrary (ordered) ring R. In this
general setting, we obtain universal machines, partial recursive functions, as well as JVP …

Structured matrices serve as a natural bridge between the areas of algebraic computations
with polynomials and numerical matrix computations, allowing cross-fertilization of both …

This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …

We present algorithms which use only O(\sqrtn) nonscalar multiplications (ie multiplications
involving “x” on both sides) to evaluate polynomials of degree n, and proofs that at least …

This book deals with various aspects of scientific numerical computing. No at tempt was
made to be complete or encyclopedic. The successful solution of a numerical problem has …

We obtain randomized algorithms for factoring degree n univariate polynomials over F_q
requiring O(n^1.5+o(1)\rmlog^1+o(1)q+n^1+o(1)\rmlog^2+o(1)q) bit operations. When …

We present an introduction to some of the state of the art in reduced order and surrogate
modeling in gravitational-wave (GW) science. Approaches that we cover include principal …

This paper develops an algorithm to multiply ap*2 matrix by a 2*n matrix in
⌈(3pn+\max(n,p))2⌉ multiplications without use of commutativity of matrix elements. The …

We give an overview of the history of fast algorithms for matrix multiplication. Along the way,
we look at some other fundamental problems in algebraic complexity like polynomial …