Bounding Hermite matrix polynomials
For the Hermite matrix polynomials H-n(x, A) in which the parameter A is a matrix whose eigenvalues lie in the open right half plane, a bound on parallel toH(n)(x,A)parallel to(2) is developed. It has the form of a simple expression in the integer n, multiplied by exp, ((5/2)parallel toAparallel to(2)x(2)), for any real x. The bound is exploited to construct an algorithm for computing any matrix exponential to within an arbitrary tolerance which may be prescribed a priori. Numerical effectiveness of the computational process is illustrated. (C) 2004 Elsevier Ltd. All rights reserved.
hermite matrix polynomials 2-norm bound