Computing Approximate Eigenpairs of Symmetric
نویسنده
چکیده
A divide-and-conquer method for computing approximate eigenvalues and eigenvectors of a block tridiagonal matrix is presented. In contrast to a method described earlier [W. N. Gansterer, R. C. Ward, and R. P. Muller, ACM Trans. Math. Software, 28 (2002), pp. 45–58], the off-diagonal blocks can have arbitrary ranks. It is shown that lower rank approximations of the off-diagonal blocks as well as relaxation of deflation criteria permit the computation of approximate eigenpairs with prescribed accuracy at significantly reduced computational cost compared to standard methods such as, for example, implemented in Lapack.
منابع مشابه
AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX
The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...
متن کاملFast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems
A fast method for enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems is proposed. Firstly theorems on verifying all eigenvalues are presented. Next a theorem on verifying all eigenvectors is presented. The proposed method is developed based on these theorems. Numerical results are presented showing the efficiency of the proposed method. As an application of ...
متن کاملShifted Power Method for Computing Tensor Eigenpairs
Abstract. Recent work on eigenvalues and eigenvectors for tensors of order m ≥ 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Axm−1 = λx subject to ‖x‖ = 1, which is closely related to optimal rank-1 approximation of a symm...
متن کاملFactorized approximate inverse preconditioning of a parallel sparse eigensolver
We exploit an optimization method, called DACG, which sequentially computes the smallest eigenpairs of a symmetric, positive deenite, generalized eigenproblem, by CG minimizations of the Rayleigh quotient over subspaces of decreasing size. In this paper we analyze the eeectiveness of the approximate inverse preconditioners, AINV and FSAI as DACG preconditioners for the solution of Finite Elemen...
متن کاملPreconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices
We propose a Preconditioned Locally Harmonic Residual (PLHR) method for computing several interior eigenpairs of a generalized Hermitian eigenvalue problem, without traditional spectral transformations, matrix factorizations, or inversions. PLHR is based on a short-term recurrence, easily extended to a block form, computing eigenpairs simultaneously. PLHR can take advantage of Hermitian positiv...
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 2003