Fast and effective algorithms are discussed for resumming matrix polynomials and Chebyshev matrix polynomials. These algorithms lead to a significant speed-up in computer time by reducing the number of matrix multiplications required to roughly twice the square root of the degree of the polynomial. A few numerical tests are presented, showing that evaluation of matrix functions via polynomial e...

Consider a convex set S = {x ∈ D : G(x) o 0} where G(x) is a symmetric matrix whose every entry is a polynomial or rational function, D ⊆ R is a domain on which G(x) is defined, and G(x) o 0 means G(x) is positive semidefinite. The set S is called semidefinite representable if it equals the projection of a higher dimensional set which is defined by a linear matrix inequality (LMI). This paper s...

We present an explicit polynomial formula for evaluating the principal logarithm of all matrices lying on the line segment {I(1 − t) + At : t ∈ [0, 1]} joining the identity matrix I (at t = 0) to any real matrix A (at t = 1) having no eigenvalues on the closed negative real axis. This extends to the matrix logarithm the well known Putzer’s method for evaluating the matrix exponential. Key-words...