The Shifted Hessenberg System Solve Computation
نویسنده
چکیده
We present methods for improving data reuse in solving sequences of linear systems that are Hessenberg matrices shifted by a sequence of scalars times the identity or a triangular matrix. The methods take into consideration the robust handling of overrow and include new condition estimation strategies. We provide timings on both scalar and vector machines to demonstrate both the diversity and importance of these ideas. We also consider the application of these ideas on a distributed computer.
منابع مشابه
Efficient Algorithm for Simultaneous Reduction to the m-Hessenberg–Triangular–Triangular Form
This paper proposes an efficient algorithm for simultaneous reduction of three matrices. The algorithm is a blocked version of the algorithm described by Miminis and Page (1982) which reduces A to the m-Hessenberg form, and B and E to the triangular form. The m-Hessenberg– triangular–triangular form of matrices A, B and E is specially suitable for solving multiple shifted systems. Such shifted ...
متن کاملControllability of the QR Algorithm on Hessenberg Flags
The shifted QR algorithm can be interpreted as a nonlinear discrete dynamical system on the flag manifold. In the complex case we describe the reachability sets as orbits of a group action and prove non-controllability of the algorithm. In contrast, the algorithm restricted on the subset of Hessenberg flags is generically controllable.
متن کاملAn index reduction method for linear Hessenberg systems
In [E. Babolian, M.M. Hosseini, Reducing index, and pseudospectral methods for differential–algebraic equations, Appl. Math. Comput. 140 (2003) 77–90] a reducing index method has been proposed for some cases of semi-explicit DAEs (differential algebraic equations). In this paper, this method is generalized to more cases. Also, it is focused on Hessenberg index 2 systems and proposed reduction i...
متن کاملOn a Distributed Design and Implementation for a Matrix Equation
We present an eecient design and implementation for the solution of the Sylvester Observer matrix equation on a distributed memory computer. It consists of two main computational intensive segments, and one of a lesser complexity: the reduction of the system matrix A to a Hessenberg form, the solution of n shifted Hessenberg systems and a number of matrix-matrix multiplies. The Hessenberg reduc...
متن کاملTransient Error Resilient Hessenberg Reduction on GPU-based Hybrid Architectures
1. ABSTRACT Graphics Processing Units (GPUs) are gaining wide spread usage in the field of scientific computing owing to the performance boost GPUs bring to computation intensive applications. The typical configuration is to integrate GPUs and CPUs in the same system where the CPUs handle the control flow and part of the computation workload, and the GPUs serve as accelerators carry out the bul...
متن کامل