A new method for computing the matrix exponential operation based on vector valued rational approximations
The authors propose a vector valued rational approximation method to compute a matrix exponential, \(e^{At}b\), where \(A\) is a complex matrix, \(t\) is a positive real number, and \(b\) is a vector. The proposed method is based on linear least-squares to evaluate the coefficients of the denominator polynomials, in which no matrix multiplications nor divisions are required. The proposed method is especially effective for fixed \(A\), \(b\), and many values of \(t\) due to a technique of scaling and recurrence. The authors also give an error analysis and numerical results.
scientific article; zbMATH DE number 6015746
scientific article