Further ways to approximate the exponential of a matrix
Titel:
Further ways to approximate the exponential of a matrix
Auteur:
Howland, James Lucien
Verschenen in:
Linear & multilinear algebra
Paginering:
Jaargang 14 (1983) nr. 2 pagina's 121-129
Jaar:
1983-10
Inhoud:
A product formula is established, and applied to approximate exp(A) in terms of the exponentials of the components of a splitting,or additive decomposition, of A. In the cases considered, these latter exponentials are given by explicit formulae. Thus, the exponentials of L, D, U in the splitting A= L + D + U are easily computed, since L and U are nilpotent and D is diagonal. A formula for the exponential of a rank one matrix is given, and may be used in conjunction with any one of a number of expressions of A as a sum of matrices of rank one. A priori estimates of the relative errors in the approximations thus obtained are supplied. The methods described were suggested by, and are extensions of the "splitting" methods described by C. Moler and C. Van Loan [SIAM Review 20 (1978), p. 826].
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