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4 papers
Computing Nearby Non-trivial Smith Forms
Mark Giesbrecht, Joseph Haraldson, George Labahn
We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to…
Computing Lower Rank Approximations of Matrix Polynomials
Mark Giesbrecht, Joseph Haraldson, George Labahn
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…
Computing Approximate Greatest Common Right Divisors of Differential Polynomials
Mark Giesbrecht, Joseph Haraldson, Erich Kaltofen
Differential (Ore) type polynomials with "approximate" polynomial coefficients are introduced. These provide an effective notion of approximate differential operators, with a stron…
Computing GCRDs of Approximate Differential Polynomials
Mark Giesbrecht, Joseph Haraldson
Differential (Ore) type polynomials with approximate polynomial coefficients are introduced. These provide a useful representation of approximate differential operators with a stro…