114,672 research outputs found
Computer programs for the solution of systems of linear algebraic equations
FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended
Algorithms for solving inverse geophysical problems on parallel computing systems
For solving inverse gravimetry problems, efficient stable parallel algorithms based on iterative gradient methods are proposed. For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, a parallel matrix sweep algorithm, a square root method, and a conjugate gradient method with preconditioner are proposed. The algorithms are implemented numerically on a parallel computing system of the Institute of Mathematics and Mechanics (PCS-IMM), NVIDIA graphics processors, and an Intel multi-core CPU with some new computing technologies. The parallel algorithms are incorporated into a system of remote computations entitled "Specialized Web-Portal for Solving Geophysical Problems on Multiprocessor Computers." Some problems with "quasi-model" and real data are solved. © 2013 Pleiades Publishing, Ltd
Automated tuning for the parameters of linear solvers
Robust iterative methods for solving systems of linear algebraic equations
often suffer from the problem of optimizing the corresponding tuning
parameters. To improve the performance for the problem of interest, the
specific parameter tuning is required, which in practice can be a
time-consuming and tedious task. The present paper deals with the problem of
automating the optimization of the numerical method parameters to improve the
performance of the mathematical physics simulations and simplify the modeling
process.
The paper proposes the hybrid evolution strategy applied to tune the
parameters of the Krylov subspace and algebraic multigrid iterative methods
when solving a sequence of linear systems with a constant matrix and varying
right-hand side. The algorithm combines the evolution strategy with the
pre-trained neural network, which filters the individuals in the new
generation. The coupling of two optimization approaches allows to integrate the
adaptivity properties of the evolution strategy with a priori knowledge
realized by the neural network. The use of the neural network as a preliminary
filter allows for significant weakening of the prediction accuracy requirements
and reusing the pre-trained network with a wide range of linear systems.
The algorithm efficiency evaluation is performed for a set of model linear
systems, including the ones from the SuiteSparse Matrix Collection and the
systems from the turbulent flow simulations. The obtained results show that the
pre-trained neural network can be reused to optimize parameters for various
linear systems, and a significant speedup in the calculations can be achieved
at the cost of about 100 trial solves. The algorithm decreases the calculation
time by more than 6 times for the black box matrices from the SuiteSparse
Matrix Collection and by a factor of 1.5-1.8 for the turbulent flow simulations
considered in the paper
Гібридний алгоритм розв’язування систем лінійних рівнянь з розрідженими матрицями методом верхньої релаксації
Розроблено і досліджено гібридні алгоритми неявного ітераційного методу розв’язування систем лінійних алгебраїчних рівнянь (СЛАР) з розрідженими симетричними додатно визначеними матрицями на основі трикутних методів: Зейделя, верхньої релаксації. Запропоновано підхід з попереднім перевпорядкуванням елементів вихідної матриці до блочно-діагональної матриці з обрамленням. Розглянуто питання програмної реалізації алгоритму на комп’ютерах з графічними процесорами.A hybrid algorithm implicit iterative method for solving systems of linear algebraic equations (SLE) with sparse symmetric positive definite matrix based on triangular methods: Seidel, over relaxation is developed and investigated. The approach of the previous rearrange elements output matrix to block-diagonal matrix of the frame is proposed. The problems of software implementation of the algorithm on a computer with a graphics processors are considered
- …