Matrix balancing and robust Monte Carlo algorithm for evaluating dominant eigenpair
نویسندگان
چکیده
Matrix balancing may effect the stability of algorithms in matrix computations and the accuracy of computed solutions. In this paper, we first introduce an algorithm for matrix balancing. Then, using Monte Carlo method we propose a robust algorithm to evaluate dominant eigenpair of a given matrix. Finally, several randomly generated examples are presented to show the efficiency of the new method.
منابع مشابه
On Finding the Smallest Generalized Eigenpair Using Markov Chain Monte Carlo Algorithm
This paper proposes a new technique based on inverse Markov chain Monte Carlo algorithm for finding the smallest generalized eigenpair of the large scale matrices. Some numerical examples show that the proposed method is efficient.
متن کاملError Analysis of a Monte Carlo Algorithm for Computing Bilinear Forms of Matrix Powers
In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the perform...
متن کاملRobustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems
In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices. Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both – systematic and probability error are presented. It is shown that the values of both errors ca...
متن کاملImplementation of Monte Carlo Algorithms for Eigenvalue Problem Using MPI
The problem of evaluating the dominant eigenvalue of real matrices using Monte Carlo numerical methods is considered. Three almost optimal Monte Carlo algorithms are presented: – Direct Monte Carlo algorithm (DMC) for calculating the largest eigenvalue of a matrix A. The algorithm uses iterations with the given matrix. – Resolvent Monte Carlo algorithm (RMC) for calculating the smallest or the ...
متن کاملMonte Carlo Numerical Treatment of Large Linear Algebra Problems
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- The Computer Science Journal of Moldova
دوره 18 شماره
صفحات -
تاریخ انتشار 2011