Condensed forms for the symmetric eigenvalue problem on multi-threaded architectures
نویسندگان
چکیده
We investigate the performance of the routines in LAPACK and the Successive Band Reduction (SBR) toolbox for the reduction of a dense matrix to tridiagonal form, a crucial preprocessing stage in the solution of the symmetric eigenvalue problem, on generalpurpose multi-core processors. In response to the advances of hardware accelerators, we also modify the code in the SBR toolbox to accelerate the computation by off-loading a significant part of the operations to a graphics processor (GPU). Performance results illustrate the parallelism and scalability of these algorithms on current high-performance multi-core and many-core architectures.
منابع مشابه
Reduction to Condensed Forms for Symmetric Eigenvalue Problems on Multi-core Architectures
We investigate the performance of the routines in LAPACK and the Successive Band Reduction (SBR) toolbox for the reduction of a dense matrix to tridiagonal form, a crucial preprocessing stage in the solution of the symmetric eigenvalue problem. The target architecture is a current general purpose multi-core processor, where parallelism is extracted using a tuned multi-threaded implementation of...
متن کاملSome results on the symmetric doubly stochastic inverse eigenvalue problem
The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$, to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$. If there exists an $ntimes n$ symmetric doubly stochastic ...
متن کاملSolution of eigenvalue problems on heterogeneous computing architectures
In this paper are presented current achievements and the state-of-the-art algorithms and implementations for dense linear algebra on traditional architectures such as single-core machines or distributed memory parallel machines. Also, this paper summarizes the current implementations and publicly available libraries for basic linear algebra for multi-core and many-core architectures (e.g. graph...
متن کاملProperties of Central Symmetric X-Form Matrices
In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.
متن کاملHardware architectures for eigenvalue computation of real symmetric matrices
Computation of eigenvalues is essential in many applications in the fields of science and engineering. When the application of interest requires the computation of eigenvalues of high throughput or realtime performance, a hardware implementation of an eigenvalue computation block is often employed. The problem of eigenvalue computation of real symmetric matrices is focused upon. For the general...
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:
- Concurrency and Computation: Practice and Experience
دوره 23 شماره
صفحات -
تاریخ انتشار 2011