Linear complexity algorithms for semiseparable matrices
Tóm tắt
Linear complexity algorithms are derived for the solution of a linear system of equations with the coefficient matrix represented as a sum of diagonal and semiseparable matrices. LDU-factorization algorithms for such matrices and their inverses are also given. The case in which the solution can be efficiently update is treated separately.
Tài liệu tham khảo
Anderson, B.D. and Moore, J.B., “Optimal Filtering”, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1979.
Carayanis, G., Kalouptsidis, N. and Manolakis, D., “Fast Recursive Algorithms for a Class of Linear Equations”, IEEE Trans. ASSP, Vol. ASSP-30, no. 2, pp. 227–239, 1982.
Gevers, M. and Kailath, T., “An Innovations Approach to Least-Squares Estimation, Part VI: Discrete-Time Innovations Representations and Recursive Estimation”, IEEE Trans. on Autom. Contr., Vol. AC-18, 6, pp. 588–600, Dec. 1973.
Gohberg, I. and Kaashoek, M., “Time Varying Linear Systems with Boundary Conditions and Integral Operators, I: The Transfer Operator and its Properties, Int. E. Op. Theory, Vol. 7, no. 3, pp. 325–391, 1984.
Gohberg, I., Kailath, T., and Koltracht, I., “Linear Systems of Equations with Recursive Structure”, Lin. Alg. and Appl. 1985, (to appear).
Gohberg, I., Kailath, T. and Koltracht, I., “Fast Matrix Factorization”, preliminary report, 1984.
Gohberg, I. and Koltracht, I., “Numerical Solutions of Integral Equations, Fast Algorithms and Krein-Sobolev Equations”, Numerische Mathematik, 1985 (to appear).
Kailath, T., “Fredholm Resolvents, Wiener-Hopf Equations, and Riccati Differential Equations”, IEEE Trans. on Inform. Theory, IT-15, no. 6, pp. 665–672, November 1969.
Kailath, T., “Some New Algorithms for Recursive Estimation in Constant Linear Systems”, IEEE Trans. on Inform. Theory, Vol. 19, no. 6, pp. 750–760, 1973.
Kailath, T., “Linear Systems”, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1980.
Kailath, T., Morf, M. and Sidhu, G.S., “Some New Algorithms for Recursive Estimation in Constant Linear Discrete-Time Systems”, Proc. Seventh Princeton Conf. on Inform. Sci. & Systs., Princeton, N.J., pp. 344–352, March 1973.
Krishna, H. and Morgera, S., “Linear Complexity Fast Algorithms for a Class of Linear Equations”, ICASSP, San Diego, CA, 1984.
Picinbono, B., “Fast Algorithms for Brownian Matrices”, IEEE Trans. ASSP, Vol. ASSP-31, pp. 512–514, April 1983.