in this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general co...

the effect of boundary conditions on the solution of the inverse problem of identifying the geometry and location of a cavity inside an elastic solid body using displacement measurements obtained from a tension test is investigated. the boundary elements method (bem) coupled with the genetic algorithm (ga) and the conjugate gradient method (cgm) are implemented in this identification problem. a...

This paper proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems Bx = b with positive definite B for x. The goal is to replace the point estimates returned by existing methods with a Gaussian posterior belief over the elements of the inverse of B, which can be used to estimate errors. Recent probabilistic interpretations of the secant family of q...

Conjugate gradient algorithms are very powerful methods for solving large-scale unconstrained optimization problems characterized by low memory requirements and strong local and global convergence properties. Over 25 variants of different conjugate gradient methods are known. In this paper we propose a fundamentally different method, in which the well known parameter k β is computed by an appro...

A descent family of Dai–Liao conjugate gradient methods Saman Babaie-Kafaki & Reza Ghanbari a Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran b School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran c Faculty of Mathematical Sciences, Ferdowsi Universi...

In this paper we present the analysis of parallelization properties of several typical preconditioners for the Conjugate Gradient methods. For implicit preconditioners, geometric and algebraic parallelization approaches are discussed. Additionally, different optimization techniques are suggested. Some implementation details are given for each method. Finally, parallel performance results are pr...

We study multigrid methods in the context of continuation methods for reaction–diffusion systems, where the Bi-CGSTAB and GMRES methods are used as the relaxation scheme for the V-cycle, W-cycle and full approximation schemes, respectively. In particular, we apply the results of Brown and Walker [1997] to investigate how the GMRES method can be used to solve nearly singular systems that occur i...

Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: 1. The Fletcher-Reeves method, the Hestenes-Stiefel method, and the Dai-Yuan method applied to a strongly convex LC objective function; 2. The Polak-Ribière method and the Conjugate ...

In this work, we propose non-linear conjugate gradient methods for finding critical points of vector-valued functions with respect to the partial order induced by a closed, convex, and pointed cone with non-empty interior. No convexity assumption is made on the objectives. The concepts of Wolfe and Zoutendjik conditions are extended for the vectorvalued optimization. In particular, we show that...