We consider the efficient and robust numerical solution of elliptic problems with jumping coefficients occurring on a network of thin fractures. We present an iterative solution concept based on a hierarchical separation of the fractures and the surrounding rock matrix. Upper estimates for the convergence rates are independent of the width of the fractures and of the jumps of the coefficients. ...

We discuss a new method for the iterative computation of a portion of the singular values and vectors of a large sparse matrix. Similar to the Jacobi-Davidson method for the eigenvalue problem, we compute in each step a correction by (approximately) solving a correction equation. It is shown that this JDSVD method can be seen as an accelerated (inexact) Newton scheme. We compare the method with...

In this paper, we first provide semi-convergence analysis for a special GPIU(Generalized Parameterized Inexact Uzawa) method with singular preconditioners for solving singular saddle point problems. We next provide a methodology of how to choose nearly quasi-optimal parameters of the special GPIU method. Lastly, numerical experiments are carried out to examine the effectiveness of the special G...

We study robustness properties of some iterative gradient-based methods for strongly convex functions, as well the larger class functions with sector-bounded gradients, under a relative error model. Proofs corresponding convergence rates are based on frequency-domain criteria stability nonlinear systems. Applications given to inexact versions gradient descent and Triple Momentum Method. To furt...

Compressed sensing (CS) demonstrates that a sparse, or compressible signal can be acquired using a low rate acquisition process below the Nyquist rate, which projects the signal onto a small set of vectors incoherent with the sparsity basis. In this paper, we propose a new framework for compressed sensing recovery problem using iterative approximation method via 0  minimization. Instead of dir...

We study an iterative low-rank approximation method for the solution of the steadystate stochastic Navier–Stokes equations with uncertain viscosity. The method is based on linearization schemes using Picard and Newton iterations and stochastic finite element discretizations of the linearized problems. For computing the low-rank approximate solution, we adapt the nonlinear iterations to an inexa...

We present a line-search algorithm for large-scale continuous optimization. The algorithm is matrix-free in that it does not require the factorization of derivative matrices. Instead, it uses iterative linear system solvers. Inexact step computations are supported in order to save computational expense during each iteration. The algorithm is an interior-point approach derived from an inexact Ne...

Parallel iterative methods are powerful tool for solving large system of linear equations (LEs). The existing parallel computing research results are focussed mainly on sparse system or others with particular structure. And most are based on parallel implementation of the classical relaxation methods such as Gauss-Seidel, SOR, and AOR methods carried efficiently on multiprcessor systems. In thi...

In each iteration of the interior point method (IPM) at least one linear system has to be solved. The main computational effort of IPMs consists in the computation of these linear systems. Solving the corresponding linear systems with a direct method becomes very expensive for large scale problems. In this thesis, we have been concerned with using an iterative method for solving the reduced KKT...

We introduce and analyze a trust–region sequential quadratic programming (SQP) method for the solution of smooth equality constrained optimization problems, which allows the inexact and hence iterative solution of linear systems. Iterative solution of linear systems is important in large-scale applications, such as optimization problems with partial differential equation constraints, where dire...