The Design of a Block Rational Lanczos Code with Partial Reorthogonalization and Implicit Restarting
نویسندگان
چکیده
We discuss the design and development of a new Fortran code EA16 for the computation of selected eigenvalues and eigenvectors of large-scale real symmetric eigenvalue problems. EA16 can be used for either the standard or the generalized eigenvalue problem. The underlying method used by EA16 is the block Lanczos method with partial reorthogonalization plus implicit restarting, combined with purging and locking of converged Ritz pairs. A spectral transformation may optionally be used. The code allows a change of pole via the rational Lanczos method. Particular attention is paid to the solution of generalized eigenvalue problems with a singular mass matrix.
منابع مشابه
An Implicitly Restarted Lanczos Bidiagonalization Method for Computing Smallest Singular Triplets
We describe the development of a method for the efficient computation of the smallest singular values and corresponding vectors for large sparse matrices [4]. The method combines state-of-the-art techniques that make it a useful computational tool appropriate for large scale computations. The method relies upon Lanczos bidiagonalization (LBD) with partial reorthogonalization [6], enhanced with ...
متن کاملA Robust and Efficient Parallel SVD Solver Based on Restarted Lanczos Bidiagonalization
Lanczos bidiagonalization is a competitive method for computing a partial singular value decomposition of a large sparse matrix, that is, when only a subset of the singular values and corresponding singular vectors are required. However, a straightforward implementation of the algorithm has the problem of loss of orthogonality between computed Lanczos vectors, and some reorthogonalization techn...
متن کاملDeflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-Hand Sides
A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is ne...
متن کاملThe Lanczos Algorithm With Partial Reorthogonalization By Horst
The Lanczos algorithm is becoming accepted as a powerful tool for finding the eigenvalues and for solving linear systems of equations. Any practical implementation of the algorithm suffers however from roundoff errors, which usually cause the Lanczos vectors to lose their mutual orthogonality. In order to maintain some level of orthogonality, full reorthogonalization (FRO) and selective orthogo...
متن کاملComputing charge densities with partially reorthogonalized Lanczos
This paper considers the problem of computing charge densities in a density functional theory (DFT) framework. In contrast to traditional, diagonalization-based, methods, we utilize a technique which exploits a Lanczos basis, without explicit reference to individual eigenvectors. The key ingredient of this new approach is a partial reorthogonalization strategy whose goal is to ensure a good lev...
متن کامل