◆ mat_power_1_norm()

template<typename EigMat1 , require_all_eigen_t< EigMat1 > * = nullptr, require_all_st_same< double, EigMat1 > * = nullptr>

double stan::math::matrix_exp_action_handler::mat_power_1_norm	(	const EigMat1 &	mat,
		int	m
	)

inline

Estimate the 1-norm of mat^m.

See A. H. Al-Mohy and N. J. Higham, A New Scaling and Squaring Algorithm for the Matrix Exponential, SIAM J. Matrix Anal. Appl. 31(3): 970-989, 2009.

For positive matrices the results is exact. Otherwise it falls back to Eigen's norm, which is only efficient for small & medium-size matrices (n < 100). Large size matrices require a more efficient 1-norm approximation algorithm such as normest1. See, e.g., https://hg.savannah.gnu.org/hgweb/octave/file/e35866e6a2e0/scripts/linear-algebra/normest1.m

Parameters

mat	matrix
m	power