Positive solutions to X = A−BX-1 B∗
Tài liệu tham khảo
Anderson, 1971, Shorted operators, SIAM J. Appl. Math., 20, 520, 10.1137/0120053
Anderson, 1969, Consistent estimates of the parameters of a linear system, Ann. Math. Statist., 40, 2064, 10.1214/aoms/1177697286
Anderson, 1979, Characterization of parallel subtraction, Proc. Nat. Acad. Sci. U.S.A., 76, 3599, 10.1073/pnas.76.8.3599
Anderson, 1983, Ladder networks, fixed points, and the geometric mean, Circuits Systems Signal Process., 3, 259, 10.1007/BF01599069
Anderson, 1988, The cascade limit, the shorted operator and quadratic optimal control, 3
Anderson, 1975, Shorted operators II, SIAM J. Appl. Math., 28, 60, 10.1137/0128007
Ando, 1978, Topics on Operator Inequalities
Ando, 1973, Structure of operators with numerical radius one, Acta Sci. Math. (Szeged), 34, 11
Ando, 1980, Limit of cascade iteration of matrices, Numer. Funct. Anal. Optim., 21, 579, 10.1080/01630563.1980.10120628
Bucy, 1972, A priori bounds for the Riccati equation, 645
Butler, 1988, A note on the shorted operator, SIAM J. Matrix Anal. Appl., 9, 147, 10.1137/0609011
C.A. Butler and T.D. Morley, Ladder networks, shorted operators and continued fractions of operators, preprint.
Carlson, 1974, A generalization of the Schur complement by means of the Moore-Penreose inverse, SIAM J. Appl. Math., 26, 254, 10.1137/0126013
H.J. Carlin and G.A. Nobel, Circuit properties of coupled dispersive lines with application to wave guide modeling, in Proceedings on Network and Signal Theory (J. K. Skwirzynski and J. O. Scanlan, Eds.), Peter Peregrinus, London, pp. 258-269.
Fujii, 1979, Arithmetic-geometric mean of operators, Math. Japon., 23, 667
Fujii, 1979, On the geometric and harmonic means of positive operators, Math. Japon., 23, 203
Green, 1985, Stabilization of linear systems over a commutative normed algebra with applications to spatially distributed parameter dependent systems, SIAM J. Control Optim., 23, 1, 10.1137/0323001
Krein, 1947, The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications, I, Mat. Sb. (N. S.), 20, 431
Krein, 1947, The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications, II, Mat. Sb. (N. S.), 21, 365
Kubo, 1980, Means of positive operators, Math. Ann., 246, 205, 10.1007/BF01371042
T. D. Morley, Shorts of block operators, Circuits Systems Signal Process, to appear.
Ouellette, 1981, Schur complements and statistics, Linear. Algebra Appl., 36, 187, 10.1016/0024-3795(81)90232-9
Pusz, 1975, Functional calculus for sequilinear forms and the purification map, Rep. Math. Phys., 8, 159, 10.1016/0034-4877(75)90061-0
W. R. S. Sutherland, H. Wolkowicz, and V. M. Zeiden, An explicit linear solution for the quadratic dynamic programming problem, preprint.
Trapp, 1984, Hermitian semidefinite matrix means and related matrix inequalities—an introduction, Linear and Multilinear Algebra, 16, 113, 10.1080/03081088408817613
Trapp, 1985, The Ricatti equation and the geometric mean, Contemp. Math., 47, 437, 10.1090/conm/047/828317
Zabezyk, 1974, Remarks on the control of discrete time distributed parameter systems, SIAM J. Control, 12, 721, 10.1137/0312056
Zemanian, 1982, Non-uniform semi-infinite grounded grids, SIAM J. Appl. Math., 13, 770, 10.1137/0513053