Sentence examples for many iterative solvers from inspiring English sources

Such a product forms the key step of many iterative solvers (such as the Krylov subspace based GMRES and BiCGSTAB) for linear systems arising from the integral equation methods for the Helmholtz equations.

When the coefficients of an elliptic problem have jumps of several orders of magnitude across an embedded interface, many iterative solvers exhibit deteriorated convergence properties or a loss of efficiency and it is difficult to achieve high solution accuracies in the whole domain.

In recent years, the iterative solvers of a large sparse linear system of equations Ax=b (1.1) are considered in many scientific computing and engineering problems, where the coefficient matrix (Ainmathcal{R}^{ntimes n}) is a nonsingular matrix, (binmathcal{R}^{n}) is a given right-hand vector, and (xinmathcal{R}^{n}) is an unknown vector.

Numerical optimization, numerical linear algebra, linear/nonlinear programming, sparse matrix methods, iterative solvers.

The numerical solution process employs adjoint models and iterative solvers.

In 3D, where the larger number of unknowns requires iterative solvers, we use a Schur-complement formulation45 to solve the velocity-pressure problem.

We show that by using our solver one can alleviate the drawbacks of direct and iterative solvers, achieving better scalability than with direct solvers and more robustness than with classical preconditioned iterative solvers.

Comparisons to well-known direct and iterative solvers on a parallel architecture are provided.

In multidimensional domains, preconditioned Krylov iterative solvers are often appropriate for these duties.

Such factorizations can be used to accelerate matrix-vector multiplications and to precondition iterative solvers.

For finite element models, iterative solvers are needed to precisely calculate eigenvectors and eigenvalues.