Browsing University of Waterloo by Supervisor "Giesbrecht, Mark"
Now showing items 1-6 of 6
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Analysis of Randomized Algorithms in Real Algebraic Geometry
(University of Waterloo, 2020-09-02)Consider the problem of computing at least one point in each connected component of a smooth real algebraic set. This is a basic and important operation in real and semi-algebraic geometry: it gives an upper bound on the ... -
Computational Approaches to Problems in Noncommutative Algebra -- Theory, Applications and Implementations
(University of Waterloo, 2016-09-28)Noncommutative rings appear in several areas of mathematics. Most prominently, they can be used to model operator equations, such as differential or difference equations. In the Ph.D. studies leading to this thesis, ... -
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 ... -
Matrix Polynomials and their Lower Rank Approximations
(University of Waterloo, 2019-08-07)This thesis is a wide ranging work on computing a “lower-rank” approximation of a matrix polynomial using second-order non-linear optimization techniques. Two notions of rank are investigated. The first is the rank as the ... -
Smith Normal Form over Local Rings and Related Problems
(University of Waterloo, 2017-08-28)The Smith normal form is a diagonalization of matrices with many applications in diophantine analysis, graph theory, system control theory, simplicial homology, and more recently, in topological analysis of big data. ... -
Sparse Polynomial Interpolation and Testing
(University of Waterloo, 2016-03-03)Interpolation is the process of learning an unknown polynomial f from some set of its evaluations. We consider the interpolation of a sparse polynomial, i.e., where f is comprised of a small, bounded number of terms. Sparse ...