Numerical Analysis, № 11, 2002

An ILU(0) modification for sparse matrices storage technique called the CSlR is discussed and briefly analyzed. Details of program implementation for the GMRES(m) preconditioning are described for C language.

We present here general principles of organization of the module "Resonance" for stochastic simulation, which is a part of the package "ACCORD", and describe basic procedures of the module for simulation of random variables.

The on-line library ACCORD includes algorithms for solving different tasks of mathematical modeling. The description of the algorithms is in the special database, which contains description of algorithms, the author software source code and executable components, which allows the users to try algorithms. The access to the library resources is...

The main topic of the paper is to present a program package to solve 3D BVP for the Helmholtz-type equation. Numerical algorithms concerning data structures, approximations, and solving are described. Structure of the input data file and the usage examples are presented. Some useful recommendations for users are given.

Two explicit incomplete factorization methods and their program implementation are presented for solution of linear algebraic systems with real symmetric positive definite (SPD) matrices. The algorithms are based on the efficient Eisenstat modification of preconditioning for the matrix row sparse format. The fast iterative convergence is provided by conjugate gradient...

The generator of M-stage modified RK-scheme, 2 < M < 21, for solving the ODE y' = f(t,y) with initial conditions and the Volterra integral equation (by the RK-method of advanced accuracy) is proposed. Modified and classical RK-methods differ for a triangular matrix B only are used.

The algorithm and the code for computing several eigenvalues and their corresponding eigenvectors of a large sparse symmetric positive definite (SPD) matrix, which arises as a result of grid approximations (FDM, FEM, or FVM) of multidimensional boundary value problems (BVPs) are described. The preconditioned inverse iteration (PINVIT) method is implemented...

The paper presents an algorithm for the numerical solution of the initial value problems for implicit systems of ordinary differential equations (ODE). The algorithm uses the Rosenbrock-type scheme with time-lagging derivative matrices, and the adaptive step size control for the global error. Some examples of solution of test problems are...

The paper introduces an algorithm for the numerical solution of initial value problems for systems of ordinary differential equations (ODE). The algorithm uses the Rosenbrock-type and the Runge-Kutta-type schemes with Jacobian freezing and automatic step size control policy based on the global error estimation. Some examples of solution of test...

The paper presents the software for the linear programming problems both for the integer and the mixed-integer linear programming. For the solution of problems of the above types it is possible to exploit a parallel algorithm. Some examples of solution of test problems are given.