In the paper we show how, based on the preconditioned Krylov subspace methods, to compute the covariance matrix of parameter estimates, which is crucial for efficient methods of optimum experimental design. Mathematics Subject Classification (2000). Primary 65K10; Secondary 15A09, 65F30.

Let P be a symmetric positive definite Pick matrix of order n. The following facts will be proven here: (a) P is the Gram matrix of a set of rational functions, with respect to a inner product defined in terms of a “generating function” associated to P ; (b) Its condition number is lower-bounded by a function growing exponentially in n; (c) P can be effectively preconditioned by the Pick matrix...

We study the solutions of Hermitian positive deenite Toeplitz systems Ax = b by the preconditioned conjugate gradient method for three families of circulant preconditioners C. The convergence rates of these iterative methods depend on the spectrum of C ?1 A. For a Toeplitz matrix A with entries which are Fourier coeecients of a positive function f in the Wiener class, we establish the invertibl...

We present a modification of a tangential frequency filtering decomposition (TFFD) preconditioner [1]. The key idea is to add a “lumping term” ch whose influence can be determined by means of Fourier analysis [2, 3]. For the standard five-point stencil, we derive an optimal order q = 4 3 , and constant c = (2π) 4 3 . With the choice of optimal order of modification, the Fourier results show tha...

A major computational issue in the finite element (FE) integration of coupled consolidation equations is the repeated solution in time of the resulting discretized indefinite system. Because of ill-conditioning, the iterative solution, which is recommended in large size 3D settings, requires the computation of a suitable preconditioner to guarantee convergence. In this paper the coupled system ...

We consider saddle-point problems that typically arise from the mixed finite element discretization of second order elliptic problems. By proper equivalent algebraic operations the considered saddle-point problem is transformed to another saddle-point problem. The resulting problem can then be efficiently preconditioned by a block-diagonal matrix or by a factored block-matrix (the blocks corres...

Abstract. In this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers and this fixe...

Cell-therapies that invoke pleiotropic mechanisms may facilitate functional recovery in stroke patients. We hypothesized that a cell therapy using microglia preconditioned by optimal oxygen-glucose deprivation (OGD) is a therapeutic strategy for ischemic stroke because optimal ischemia induces anti-inflammatory M2 microglia. We first delineated changes in angiogenesis and axonal outgrowth in th...

Boundary value methods (BVMs) for ordinary di erential equations require the solution of nonsymmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A block-circulant preconditioner with circulant blocks (BCCB preconditioner) is proposed to speed up the convergence rate of the GMRES method. The BCCB preconditio...