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math.NA2022
Contour Integration for Eigenvector Nonlinearities
Rob Claes, Karl Meerbergen, Simon Telen
Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonline…
math.NA2020
Backward Error Measures for Roots of Polynomials
Simon Telen, Sascha Timme, Marc Van Barel
We analyze different measures for the backward error of a set of numerical approximations for the roots of a polynomial. We focus mainly on the element-wise mixed backward error in…
math.NA2020
Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers
Simon Telen, Marc Van Barel, Jan Verschelde
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on powe…