Browsing Mathematics (Faculty of) by Supervisor "Storjohann, Arne"
Now showing items 1-4 of 4
-
Computing a Basis for an Integer Lattice
(University of Waterloo, 2022-12-22)The extended gcd problem takes as input two integers, and asks as output an integer linear combination of the integers that are equal to their gcd. The classical extended Euclidean algorithm and fast variants such as the ... -
Computing Matrix Canonical Forms of Ore Polynomials
(University of Waterloo, 2017-05-01)We present algorithms to compute canonical forms of matrices of Ore polynomials while controlling intermediate expression swell. Given a square non-singular input matrix of Ore polynomials, we give an extension of the ... -
Fast algorithms for computing with integer matrices: normal forms and applications
(University of Waterloo, 2021-09-24)The focus of this thesis is on fundamental computational problems in exact integer linear algebra. Specifically, for a nonsingular integer input matrix A of dimension n, we consider problems such as linear system solving ... -
Faster Algorithms for Sparse Decomposition and Sparse Series Solutions to Differential Equations
(University of Waterloo, 2022-05-09)Sparse polynomials are those polynomials with only a few non-zero coefficients relative to their degree. They can appear in practice in polynomial systems as inputs, where the degree of the input sparse polynomial can be ...