Computing exponentials of essentially non-negative matrices entrywise to high relative accuracy
Jungong Xue, Qiang Ye · Mathematics of Computation · 2013
A real square matrix is said to be essentially non-negative if all of its off-diagonal entries are non-negative. It has recently been shown that the exponential of an essentially non-negative matrix is determined entrywise to high relative accuracy by its entries up to a condition number intrinsic to the exponential function (Numer. Math. 110 (2008), 393–403). Thus the smaller entries of the exponential may be computed to the same relative accuracy as the bigger entries. This paper develops algorithms to compute exponentials of essentially non-negative matrices entrywise to high relative accuracy.