Computing $f(A)b$ for Matrix Functions $f$

For matrix functions $f$ we investigate how to compute a matrix-vector product $f(A)b$ without explicitly computing $f(A)$. A general method is described that applies quadrature to the matrix version of the Cauchy integral theorem. Methods specific to the logarithm, based on quadrature, and fractional matrix powers, based on solution of an ordinary differential equation initial value problem, are also presente