Monte Carlo Numerical Treatment of Large Linear Algebra Problems
نویسندگان
چکیده
In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces. Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.
منابع مشابه
Fast Randomized Iteration: Diffusion Monte Carlo through the Lens of Numerical Linear Algebra
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of randomized iterative algorithms based on similar principles to address a variety of common tasks in numerical linear algebra. From the point of view of numerical li...
متن کاملParallel resolvent Monte Carlo algorithms for linear algebra problems
In this paper we consider Monte Carlo (MC) algorithms based on the use of the resolvent matrix for solving linear algebraic problems. Estimates for the speedup and efficiency of the algorithms are presented. Some numerical examples performed on cluster of workstations using MPI are given.
متن کاملA Monte Carlo method for solving unsteady adjoint equations
Traditionally, solving the adjoint equation for unsteady problems involves solving a large, structured linear system. This paper presents a variation on this technique and uses a Monte Carlo linear solver. The Monte Carlo solver yields a forward-time algorithm for solving unsteady adjoint equations. When applied to computing the adjoint associated with Burgers’ equation, the Monte Carlo approac...
متن کاملRobust and Efficient Numerical Linear Algebra Solvers and Applications in Quantum Mechanical Simulations
Optimization of large scale linear algebra computations is a long-standing problem in numerical analysis and scientific computing communities. In this pape, we describe our recent synergistic effort on the development of robust, accurate and efficient linear algebra techniques and applications to quantum mechanical simulation. We demonstrate the feasibility, through the use of newly developed l...
متن کاملStudy of Preconditioners based on Markov Chain Monte Carlo Methods
Nowadays, analysis and design of novel scalable methods and algorithms for fundamental linear algebra problems such as solving Systems of Linear Algebraic Equations with focus on large scale systems is a subject of study. This research focuses on the study of novel mathematical methods and scalable algorithms for computationally intensive problems such as Monte Carlo and Hybrid Methods and Algo...
متن کامل