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C++ API

: expm (A)

Return the exponential of a matrix.

The matrix exponential is defined as the infinite Taylor series

expm (A) = I + A + A^2/2! + A^3/3! + …

However, the Taylor series is not the way to compute the matrix exponential; see Moler and Van Loan, Nineteen Dubious Ways to Compute the Exponential of a Matrix, SIAM Review, 1978. This routine uses Ward’s diagonal Padé approximation method with three step preconditioning (SIAM Journal on Numerical Analysis, 1977). Diagonal Padé approximations are rational polynomials of matrices

     -1
D (A)   N (A)

whose Taylor series matches the first 2q+1 terms of the Taylor series above; direct evaluation of the Taylor series (with the same preconditioning steps) may be desirable in lieu of the Padé approximation when Dq(A) is ill-conditioned.

See also: logm, sqrtm.

Package: octave