Resolvent expansions of matrices and applications. (English) Zbl 0468.15002

Rothblum, Uriel G.

Linear Algebra Appl. 38, 33-49 (1981).

MSC:

15A09	Theory of matrix inversion and generalized inverses
15A18	Eigenvalues, singular values, and eigenvectors
15A99	Basic linear algebra

Keywords:

spektral radius; resolvent expansion; perturbation expansion; M-matrix; Drazin inverse; eigenprojection

References:

[1]	Berman, A.; Plemmons, R.J., Nonnegative matrices in the mathematical sciences, (1979), Academic New York · Zbl 0484.15016
[2]	Blackwell, D., Discrete dynamic programming, Ann. math. statist., 33, 719-726, (1962), (1962) · Zbl 0133.12906
[3]	B. C. Eaves and U. G. Rothblum, Homotopies for piecewise linear equations in ordered fields with applications to an invariant curve theorem, in preparation.
[4]	Gantmacher, F.R., The theory of matrices, (1971), K.A. Hirsh Chelsea, New York, trans. from Russian by · Zbl 0085.01001
[5]	Halmos, P.R., Finite dimensional vector spaces, (1958), Van Nostrand Princeton, N.J · Zbl 0107.01404
[6]	Hardy, G., Divergent series, (1949), Clarendon Oxford · Zbl 0032.05801
[7]	Jeroslow, R.G., Linear programs dependent on a single parameter, Discrete math., 6, 119-140, (1973) · Zbl 0283.90029
[8]	Kato, T., Pertubation theory for linear operators, (1966), Springer New York
[9]	Knopp, K., Theory and applications of infinite series, (1951), Hafner New York, (transl. by R. C. H. Young)
[10]	Meyer, C.D., Limits and the index of a square matrix, SIAM J. appl. math., 26, 469-478, (1974) · Zbl 0249.15004
[11]	Meyer, C.D., An alternative expression for the Mean first passage matrix, Linear algebra and appl., 22, 41-47, (1978) · Zbl 0401.60063
[12]	Meyer, C.D., The condition of a finite Markov chain and pertubation bounds for the limiting probabalities, 24, (1979), unpublished manuscript
[13]	Meyer, C.D.; Rose, N.J., The index and Drazin inverse of block triangular matrices, SIAM J. appl. math., 33, 1-7, (1977) · Zbl 0355.15009
[14]	Meyer, C.D.; Stadelmaier, M.W., Singular M-matrices and inverse positivity, Linear algebra and appl., 22, 139-156, (1978) · Zbl 0411.15006
[15]	Miller, B.L.; Veinott, A.F., Discrete dynamic programming with a small interest rate, Ann. math. statist., 40, 366-370, (1969) · Zbl 0175.47302
[16]	Plemmons, R.J., M-matrices leading to semi-convergent splittings, Linear algebra and appl., 15, 243-252, (1976) · Zbl 0358.15016
[17]	Rothblum, U.G., Normalized Markov decision chains I: sensitive discount optimality, Operations res., 23, 785-795, (1975) · Zbl 0318.90023
[18]	Rothblum, U.G., A representation of the Drazin inverse and characterizations of the index, SIAM J. applied math., 31, 646-648, (1976) · Zbl 0355.15008
[19]	Rothblum, U.G.; Wets, Roger J.-B., A computation of the eigenprojection of a nonnegative matrix at its spectral radius, Mathematical programming studies 6, stochastic systems: modeling, identification and optimization II, 188-201, (1976)
[20]	Rothblum, U.G., An index classification of M-matrices, Linear algebra and appl., 23, 1-12, (1979) · Zbl 0402.15009
[21]	Rothblum, U.G., Expansion of partial sums of matrix powers, SIAM rev., 23, 2, (April 1981)
[22]	U. G. Rothblum, and A. F. Veinott, Branching Markov decision chains, in preparation.
[23]	Varga, R.S., Matrix iterative analysis, (1962), Prentice-Hall Englewood Cliffs, N.J · Zbl 0133.08602
[24]	Vandergraft, J.S., Spectral properties of matrices which have invariant cones, SIAM J. appl. math., 16, 1208-1222, (1968) · Zbl 0186.05701
[25]	Veinott, A.F., Discrete dynamic programming with sensitive discount optimality criteria, Ann. math. statist., 40, 1635-1660, (1969) · Zbl 0183.49102