Preconditioning is the most common approach for accelerating an iterative method and consists in solving an auxilliary problem structurally close to the original one. In most situations, the art of preconditioning consists in building in a efficient way a matrix or a sequence of matrices. This explicit approach is not however always possible and there are situations in which preconditioned vers...

In this paper, we propose a new fast Fourier transform (FFT) based LMS-Newton (LMSN) adaptive filter algorithm. At each adaptive time step t, the nth-order filter coefficients are updated by using the inverse of an n-by-n Hermitian, positive definite, Toeplitz operator T (t). By applying the cyclic displacement formula for the inverse of a Toeplitz operator, T (t)−1 can be constructed using the...

We propose a modified alternating positive semidefinite splitting (MAPSS) preconditioner for solving block three-by-three saddle point problems that arise in linear programming and the finite element discretization of Maxwell equations. Spectral properties MAPSS-preconditioned matrix are discussed analyzed detail. As efficiency MAPSS depends on its parameters, we derive fast effective formulas ...

and Kk(BA,Br) = span{Br, (BA)Br, . . . , (BA)k−1Br}, (3) where B ∈ Rn×m is the mapping and preconditioning matrix, and apply Krylov subspace iteration methods on these subspaces. For overdetermined problems, applying the standard CG method to Kk(BA,Br) leads to the preconditioned CGLS [3] or CGNR [9] method while for underdetermined problems it leads to preconditioned CGNE [9] method. The GMRES...

Dedicated to Alan George on the occasion of his 60th birthday Abstract. The splitting lemma is one of the two main tools of support theory, a framework for bounding the condition number of definite and semidefinite preconditioned linear systems. The splitting lemma allows the analysis of a complicated system to be partitioned into analyses of simpler systems. The other tool is the symmetric-pro...

Explicit pre/post conditioning of the large, sparse and non-symmetric system of equations, arising from the discretization of the Dirichlet Poisson’s Boundary Value Problem (BVP) by the Hermite Collocation method is the problem considered herein. Using the 2-cyclic (red-black) structure of the Collocation coefficient matrix, we investigate the eigenvalue distribution of its preconditioned analo...

We propose to compute the search direction at each interior-point iteration for a linear program via a reduced augmented system that typically has a much smaller dimension than the original augmented system. This reduced system is potentially less susceptible to the ill-conditioning effect of the elements in the (1, 1) block of the augmented matrix. A preconditioner is then designed by approxim...

This paper deals with convergence estimates of GMRES(m) [Saad and Schultz, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856–869] preconditioned by multigrid [Brandt, Math. Comp., 31 (1977), pp. 333–390], [Hackbusch, Multi-Grid Methods and Applications, Springer, Berlin, 1985]. Fourier analysis is a well-known and useful tool in the multigrid community for the prediction of two-grid convergence ...

BACKGROUND Vasculogenic mimicry (VM), as a new blood supply for tumor growth and hematogenous metastases, has been recently described in highly aggressive human melanoma cells, etc. We previously reported VM in human gallbladder carcinomas and its clinical significance. In this study, we further studied histomorphology and hemodynamic of VM in gallbladder carcinomas in vivo and in vitro. METH...

The discretization of eigenvalue problems for partial differential operators is a major source of matrix eigenvalue problems having very large dimensions, but only some of the smallest eigenvalues together with the eigenvectors are to be determined. Preconditioned inverse iteration (a “matrix factorization–free” method) derives from the well–known inverse iteration procedure in such a way that ...