AbRtract This paper deals with the domain decomposition-based preconditioned conjugate gradient method. The Schur complement is expressed as a function of & simple interface matrix. This function is approximated by a simple rational function to generate a simple matrix that is then used 8.8 & preconditioner for the Schur complement. Extensive experiments are performed to examine the effectivene...

The Conjugate Gradient (CG) method is often used to solve a positive definite linear system Ax = b. This paper analyzes two hard cases for CG or any Krylov subspace type methods by either analytically finding the residual formulas or tightly bound the residuals from above and below, in contrast to existing results which only bound residuals from above. The analysis is based on a general framewo...

This paper is concerned with the numerical solution of a Karush–Kuhn– Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior–Point (IP) approach. In this framework, we discuss the effectiveness of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the implementation deta...

We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = ∑ aij(x)uxixj + ∑ bi(x)uxi + c(x)u. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a separable operator, and prove that the res...

A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenvalues of the preconditioned system. These eigenvalues can be bounded independently of the mesh size...

We present an efficient multigrid algorithm that is adequate to solve a heavy linear system given in cloth simulation. Although multigrid has been successfully applied to the Poisson problems, it is hard to migrate to complicated cloth deformations due to its lack of physical meaning in level construction. We addresses this problem by developing a physically faithful technique ensuring the cons...

This paper studies the use of a generalized hierarchical basis transformation at each level of a multilevel block factorization. The factorization may be used as a preconditioner to the conjugate gradient method, or the structure it sets up may be used to define a multigrid method. The basis transformation is performed with an averaged piecewise constant interpolant and is applicable to unstruc...

Abstract Background A simple, robust, precise, and an accurate HPLC method was established for simultaneous estimation of xylometazoline hydrochloride ipratropium bromide from a nasal spray dosage form. The effective separation obtained by injecting 10 μl sample standard solutions on to Inertsil ODS column, 250 × 4.6, mm, 5 μ at 45 °C using phosphate buffer with 1-pentane sulphonic acid sodium ...

We present a practical approach for solving volume and surface mesh optimization problems. Our approach is based on Newton’s method which uses both first-order (gradient) and second-order (Hessian) derivatives of the nonlinear objective function. The volume and surface optimization algorithms are modified such that surface constraints and mesh validity are satisfied. We also propose a simple an...

The basic conjugate gradient method for unconstrained optimal control problems was proposed by Lasdon et al. in [1]. The penalty function approach to the solution of inequality constrained optimal control problems has been considered in [2] and the clipping-off technique that solves optimal control problems with magnitude constraint on the control inputs is described in [3, 4]. The proposed alg...