While the computation of the matrix exponential is known to be dubious, the computed value is used widely in system analysis. This is especially true for the time-dependent matrix exponential. As the systems that we model become more complex, the order of the systems, and thus the order of the matrix exponential become larger. Even with today’s increases in processing power, the computation of ...

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 a series with matrix coefficients, and provide a characterization for when the matrix series is regular based on the algebraic variety of an ...

A sequence of increasingly refined interpolation grids inside the tetrahedron is proposed with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The number of interpolation nodes, N , corresponds to the number of terms in the complete mth-order polynomial expansion with respect to the three tetrahedral barycentric coordinates. The proposed grid is constructed b...

By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is spread out since the resulting interpolation matrix is sparse and thus eecient solvers can be used. In this paper we study locally supported kernels in detail. Investigations on the Legendre coeecients allow a characterization of the underlying Hilbert space struc...