时间（Datetime） 2014-10-31 9:00-10:00
单位（Affiliation） Laboratoire Paul Painlev ́e University of Lille, France
报告人（Speaker） Claude Brezinski
The moments cn = (z,Anz) of a matrix A have important applications in numerical linear algebra .They have been used for estimating the norm of the error in the solution of systems of linear equations , and in the choice of the parameter in Tikhonov regularization method [3,4]. They also lead to estimations of Tr(A−1) , and to estimates of the trace of Aq, for q ∈ Q . Extensions to (z, A−1y) and (z, f(A)z) can also be studied . All these estimates are obtained by extrapolation of the moments of A. Numerical results are given, and applications are discussed.
 G.H. Golub, G. Meurant, Matrices, Moments and Quadrature with Ap- plications, Princeton University Press, Princeton, 2010.
 C. Brezinski, Error estimates for the solution of linear systems, SIAM J. Sci. Comput., 21 (1999) 764–781.
 C. Brezinski, G. Rodriguez, S. Seatzu, Error estimates for linear systems with applications to regularization, Numer. Algorithms, 49 (2008) 85-104.
 C. Brezinski, M. Redivo–Zaglia, G. Rodriguez, S. Seatzu, Multi–parameter regularization techniques for ill–conditioned linear systems, Numer. Math., 94 (2003) 203-228.
 C. Brezinski, P. Fika, M. Mitrouli, Moments of a linear operator on a Hilbert space, with applications to the trace of the inverse of matrices and the solution of equations, Numer. Linear Algebra Appl., 19 (2012) 937-953.
 C. Brezinski, P. Fika, M. Mitrouli, Estimations of the trace of powers of positive self–adjoint operators by extrapolation of the moments, Electr. Trans. Numer. Anal., 39 (2012) 144-159.
 P. Fika, M. Mitrouli, P. Roupa, Estimates for the bilinear form xT A−1y with applications to linear algebra problems, Electr. Trans. Numer. Anal., to appear.