Using MPI on PC Cluster to Compute Eigenvalues of Hermitian Toeplitz Matrices
نویسندگان
چکیده
In this paper MPI is used on PC Cluster to compute all the eigenvalues of Hermitian Toeplitz Matrices. The parallel algorithms presented were implemented in C++ with MPI functions inserted and run on a cluster of Lenovo ThinkCentre machines running RedHat Linux. The two methods, MAHT-P one embarrassingly parallel and the other MPEAHT using master/ slave scheme are compared for performance and results presented. It is seen that computation time is reduced and speedup factor increases with the number of computers used for the two parallel schemes presented. Load balancing becomes an issue as number of computers in a cluster are increased. A solution is provided to overcome such a case.
منابع مشابه
Localization of the Eigenvalues of Toeplitz
This paper explores the relationship between Toeplitz and circulant matrices. Upper and lower bounds for all eigenvalues of hermitian Toeplitz matrices are given, capitalizing on the possibility of embedding a Toeplitz matrix in a circulant, and of expressing any nn Toeplitz matrix as a sum of two matrices with known eigenvalues. The bounds can be simultaneously found using a single discrete Fo...
متن کاملInside the eigenvalues of certain Hermitian Toeplitz band matrices
While extreme eigenvalues of large Hermitian Toeplitz matrices have been studied in detail for a long time, much less is known about individual inner eigenvalues. This paper explores the behavior of the jth eigenvalue of an n-by-n banded Hermitian Toeplitz matrix as n goes to infinity and provides asymptotic formulas that are uniform in j for 1 ≤ j ≤ n. The real-valued generating function of th...
متن کاملEigenvalues of Hermitian Toeplitz matrices
The paper is concerned with finite Hermitian Toeplitz matrices whose entries in the first row grow like a polynomial. Such matrices cannot be viewed as truncations of an infinite Toeplitz matrix which is generated by an integrable function or a nice measure. The main results describe the first-order asymptotics of the extreme eigenvalues as the matrix dimension goes to infinity and also deliver...
متن کاملA Note on Computing Eigenvalues of Banded Hermitian Toeplitz Matrices
It is pointed out that the author's O(n 2) algorithm for computing individual eigenvalues of an arbitrary n × n Hermitian Toeplitz matrix T n reduces to an O(rn) algorithm if T n is banded with bandwidth r.
متن کاملPreconditioners for Non-hermitian Toeplitz Systems 1
In this paper, we construct new !-circulant preconditioners for non-Hermitian Toeplitz systems, where we allow the generating function of the sequence of Toeplitz matrices to have zeros on the unit circle. We prove that the eigenvalues of the preconditioned normal equation are clustered at 1 and that for (N; N)-Toeplitz matrices with spectral condition number O(N) the corresponding PCG method r...
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:
دوره شماره
صفحات -
تاریخ انتشار 2010