Lanczos tridiagonalization and core problems
نویسندگان
چکیده
منابع مشابه
Block Lanczos Tridiagonalization of Complex Symmetric Matrices
The classic Lanczos method is an effective method for tridiagonalizing real symmetric matrices. Its block algorithm can significantly improve performance by exploiting memory hierarchies. In this paper, we present a block Lanczos method for tridiagonalizing complex symmetric matrices. Also, we propose a novel componentwise technique for detecting the loss of orthogonality to stablize the block ...
متن کاملParallel Bandreduction and Tridiagonalization
This paper presents a parallel implementation of a blocked band reduction algorithm for symmetric matrices suggested by Bischof and Sun. The reduction to tridiagonal or block tridiagonal form is a special case of this algorithm. A blocked double torus wrap mapping is used as the underlying data distribution and the so-called WY representation is employed to represent block orthogonal transforma...
متن کاملA Filtered Lanczos Procedure for Extreme and Interior Eigenvalue Problems
When combined with Krylov projection methods, polynomial filtering can provide a powerful method for extracting extreme or interior eigenvalues of large sparse matrices. This general approach can be quite efficient in the situation when a large number of eigenvalues is sought. However, its competitiveness depends critically on a good implementation. This paper presents a technique based on such...
متن کاملParallelization of the Lanczos Algorithm on Multi-core Platforms
In this paper, we report our parallel implementations of the Lanczos sparse linear system solving algorithm over large prime fields, on a multi-core platform. We employ several load-balancing methods suited to these platforms. We have carried out process-level and threadlevel parallel implementations under two different arithmetic libraries, and the best speedup obtained is 6.57 on eight cores....
متن کاملGMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems
The GMRES and Arnoldi algorithms, which reduce to the CR and Lanczos algorithms in the symmetric case, both minimize p(A)b over polynomials p of degree n. The difference is that p is normalized at z 0 for GMRES and at z x for Arnoldi. Analogous "ideal GMRES" and "ideal Arnoldi" problems are obtained if one removes b from the discussion and minimizes p(/l)II instead. Investigation of these true ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.05.006