Lectures on Numerical Linear Algebra by Prof. Lothar Reichel
March 6th (Tuesday)
National Institute of Informatics
Room 1212 (Lecture room 1), 12th floor
Professor Lothar Reichel
Department of Mathematical Sciences, Kent State University, USA
Generalized Krylov subspace methods for l_p-l_q minimization with application to image restoration.
This talk presents new efficient approaches for the solution of l_p-l_q minimization problems based on the application of successive orthogonal projections onto generalized Krylov subspaces of increasing dimension. The subspaces are generated according to the iteratively reweighted least-squares strategy for the approximation of
l_p- and l_q-norms (or quasi-norms for 0<p,q<1) by using weighted l_2-norms. Computed image restoration examples illustrate the performance of the methods discussed. The talk presents joint work with A. Buccini, G.-X. Huang, A. Lanza, S. Morigi, and F. Sgallari.
Some structured matrix problems in Gauss-type quadrature
It is well-known that Gauss quadrature rules can be computed by evaluating the integrand at a symmetric tridiagonal matrix determined by recursion coefficients of orthogonal polynomials associated with the underlying measure. This talk describes several generalizations that can be applied to approximate certain matrix functions and estimate the error in the approximations so determined. These generalizations involve symmetric and nonsymmetric tridiagonal and block tridiagonal matrices. The talk presents joint work with H. Alqahtani and M. Pranic'.
hayami [at] nii.ac.jp