Abstract
It is shown that for certain classes of infinite block Toeplitz matricesT(a)=[a j-k ] ∞0 the Moore-Penrose inverses of the finite sectionT n (a)=[a j-k ] n−10 converge to the Moore-Penrose inverse ofT(a). Furthermore the convergence for modified finite section methods and the finite section method for Wiener-Hopf integral and related operators are studied.
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References
[B] N.Bowers, Toeplitz forms associated with matrix valued functions, Thesis, Univ. of Minnesota, 1965.
[BGK] H.Bart, I.Gohberg, and M.A.Kaashoek, The coupling method for solving integral equations, in:Topics in Operator Theory and Networks (H.Dym and I.Gohberg, eds.), Operator Theory: Advances and Applications, Vol. 12, Birkhäuser, Basel, 1984, 39–73.
[BS] A.Böttcher and B.Silbermann,Analysis of Toeplitz Operators, Akademie-Verlag, Berlin, 1987, Springer, New York, Heidelberg, Berlin, 1990.
[BT] H.Bart and V.E.Tsekanovskii, Matricial Coupling and Equivalence After Extension, InOperator Theory: Advances and Applications, Vol. 59, Birkhäuser, Basel, Boston, Berlin, 1992, 143–159.
[CG] K.F.Clancey and I.Gohberg,Factorization of Matrix Functions and Singular Integral Operators, Birkhäuser, Basel, Boston, Stuttgart, 1981.
[Ch] I.S.Chebotaru, The reduction of systems of Wiener-Hopf equations to systems with vanishing indices, (Russian),Bull. Akad. Shtiince RSS Moldoven. 8 (1967), 54–66.
[GF] I.C.Gohberg and I.A.Feldman,Convolution equations and projection methods for their solution, Transl. Math. Monographs, vol. 41, Amer. Math. Soc., Providence, R. I., 1974.
[GGK] I.Gohberg, S.Goldberg and M.A.Kaashoek,Classes Of Linear Operators Vol. I, Birkhäuser, Basel, Boston, Berlin, 1990.
[H1] G.Heinig, Endliche Toeplitzmatrizen und zweidimensionale Wiener-Hopf-Operatoren mit homogenem Symbol,Mathematische Nachrichten, 82 (1978), 29–68.
[H2] G.Heinig, Partial indices of Toeplitz-like operators,Integral Equations and Operator Theory, 8 (1985), 805–824.
[H3] G.Heinig, Generalized inverses of Hankel and Toeplitz mosaic matrices,Linear Algebra Appl., to appear.
[HH] G.Heinig and F.Hellinger, Displacement structure of pseudo-inverses,Linear Algebra Appl., to appear.
[HJ] G.Heinig and P.Jankowski, Kernel structure of block Hankel and Toeplitz matrices and partial realization,Linear Algebra Appl. 175 (1992), 1–32.
[HR] G.Heinig and K.Rost,Algebraic Methods for Toeplitz-like Matrices and Operators, Akademie-Verlag, Berlin, and Birkhäuser, Basel, Boston, Stuttgart, 1984.
[Hi] I.I.Hirschman, Matrix valued Toeplitz operators,Duke Math. J. 34 (1967), No. 3, 403–415.
[KS] A.V.Kozak and I.B.Simonenko, Projection methods for the solution of multivariate discrete convolution equations, (Russian),Sibirsk. Mat. Zh. vol. XXI (1980), no. 2, 119–127.
[PS] S.Prößdorf and B.Silbermann,Numerical Analysis For Integral And Related Operator Equations, Birkhäuser, Basel, Boston, Stuttgart, Akademie-Verlag, Berlin, 1991.