This article continues prior work of the authors on the combined a posteriori analysis for the discretization and iteration errors in the finite element approximation of linear elliptic problems to the nonlinear case. The underlying theoretical framework is again that of the Dual Weighted Residual (DWR) method for goal-oriented error control. The accuracy in the algebraic solution process can b...

No part of the Journal may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission from Summary Shifted linear systems are of the form (A − σ k I)x k = b, (1) where A ∈ C N ×N , b ∈ C N and {σ k } Nσ k=1 ∈ C is a sequence of numbers, called shifts. In order to so...

the relations of fibrolite-biotite are discussed by presenting data from the ardara aureole, nw ireland. biotite-fibrolite intergrowths are developed in all three aureole zones including: the outer kyanite-bearing andalusite zone, the middle kyanite-free andalusite zone and the inner prismatic sillimanite zone. a strain-assisted mechanism is proposed for the fibrolitisation of biotite in the ar...

In this paper, a new multi-parameter iterative algorithm is proposed to address the PageRank problem based on multi-splitting iteration method. The method solves two linear subsystems at each by splitting coefficient matrix, considering therefore inner and outer find approximate solutions of these subsystems. It can be shown that sequence generated finally converges vector when parameters satis...

The Lanczos method is an iterative procedure to compute an orthogonal basis for the Krylov subspace generated by a symmetric matrix A and a starting vector v. An interesting application of this method is the computation of the matrix exponential exp(−τA)v. This vector plays an important role in the solution of parabolic equations where A results from some form of discretization of an elliptic o...

Linearly constrained optimization problems with simple bounds are considered in the present work. First, a preconditioned spectral gradient method is defined for the case in which no simple bounds are present. This algorithm can be viewed as a quasiNewton method in which the approximate Hessians satisfy a weak secant equation. The spectral choice of steplength is embedded into the Hessian appro...

The stress wave propagation in a generalized thermoelastic polygonal plate of inner and outer cross sections is studied using the Fourier expansion collocation method. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermoelastic plate of polygonal shape, composed of homogeneous isotropic material.  The freque...

For the solution of large sparse nonnegative constrained least squares (NNLS) problems, a new iterative method is proposed which uses the CGLS method for the inner iterations and the modulus iterative method for the outer iterations to solve the linear complementarity problem resulting from the Karush-Kuhn-Tucker condition of the NNLS problem. Theoretical convergence analysis including the opti...

A domain decomposition method with Lagrange multipliers for the Stokes problem is developed and analysed. A common approach to solve the Stokes problem, termed the Uzawa algorithm, is to decouple the velocity and the pressure. This approach yields the Schur complement system for the pressure Lagrange multiplier which is solved with an iterative solver. Each outer iteration of the Uzawa procedur...