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学术预告:Claude Brezinski谈:“Some applications of moments in numerical linear algebra ”

来源 :      作者 : 沈冬杰     时间 : 2014-10-29  访问量 : 50

时间(Datetime   2014-10-31 9:00-10:00

地点(Venue     下沙校区第三实验楼二楼东会议室

单位(Affiliation Laboratoire Paul Painlev ́e University of Lille, France

报告人(Speaker Claude  Brezinski

摘要(Abstract

The moments cn = (z,Anz) of a matrix A have important applications in numerical linear algebra [1].They have been used for estimating the norm of the error in the solution of systems of linear equations [2], and in the choice of the parameter in Tikhonov regularization method [3,4]. They also lead to estimations of Tr(A−1) [5], and to estimates of the trace of Aq, for q Q [6]. Extensions to (z, A−1y) and (z, f(A)z) can also be studied [7]. All these estimates are obtained by extrapolation of the moments of A. Numerical results are given, and applications are discussed.

References

[1] G.H. Golub, G. Meurant, Matrices, Moments and Quadrature with Ap- plications, Princeton University Press, Princeton, 2010.

[2] C. Brezinski, Error estimates for the solution of linear systems, SIAM J. Sci. Comput., 21 (1999) 764–781.

[3] C. Brezinski, G. Rodriguez, S. Seatzu, Error estimates for linear systems with applications to regularization, Numer. Algorithms, 49 (2008) 85-104.

[4] C. Brezinski, M. Redivo–Zaglia, G. Rodriguez, S. Seatzu, Multi–parameter regularization techniques for ill–conditioned linear systems, Numer. Math., 94 (2003) 203-228.

[5] 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.

[6] 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.

[7] 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.

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