Browsing Mathematics (Faculty of) by Author "Haraldson, Joseph"

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Computing Approximate GCRDs of Differential Polynomials

Haraldson, Joseph (University of Waterloo, 2015-09-21)

We generalize the approximate greatest common divisor problem to the non-commutative, approximate Greatest Common Right Divisor (GCRD) problem of differential polynomials. Algorithms for performing arithmetic on approximate ...
Computing lower rank approximations of matrix polynomials

Giesbrecht, Mark; Haraldson, Joseph; Labahn, George (Elsevier, 2020-05)

Given an input matrix polynomial whose coefficients are floating point numbers, we consider the problem of finding the nearest matrix polynomial which has rank at most a specified value. This generalizes the problem of ...
Matrix Polynomials and their Lower Rank Approximations

Haraldson, Joseph (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 ...