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ACMS Applied Math Seminar: Nathan Bliss

Thu Mar 9, 2017 3:30PM - 4:30PM • Calendars: Applied Math Seminar

Nathan Bliss
University of Illinois, Chicago
 

3:30 PM
154 Hurley

The Method of Gauss-Newton to Compute Power Series Solutions of Polynomial Homotopies

We consider the extension of the method of Gauss-Newton from complex floating-point arithmetic to the field of truncated power series with complex floating-point coefficients. With linearization we formulate a linear system where the coefficient matrix is instead a series with matrix coefficients. We show that in the regular case, the solution of the linear system satisfies the conditions of the Hermite interpolation problem. In general, we solve a Hermite-Laurent interpolation problem, via a lower triangular echelon form on the coefficient matrix. We conclude with a few illustrative examples, with an eye toward homotopy continuation.

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