On Mixed Precision Iterative Refinement for Eigenvalue Problems
نویسندگان
چکیده
منابع مشابه
Parallel iterative refinement in polynomial eigenvalue problems
Methods for the polynomial eigenvalue problem sometimes need to be followed by an iterative refinement process to improve the accuracy of the computed solutions. This can be accomplished by means of a Newton iteration tailored to matrix polynomials. The computational cost of this step is usually higher than the cost of computing the initial approximations, due to the need of solving multiple li...
متن کاملGPU-Accelerated Asynchronous Error Correction for Mixed Precision Iterative Refinement
In hardware-aware high performance computing, blockasynchronous iteration and mixed precision iterative refinement are two techniques that are applied to leverage the computing power of SIMD accelerators like GPUs. Although they use a very different approach for this purpose, they share the basic idea of compensating the convergence behaviour of an inferior numerical algorithm by a more efficie...
متن کاملIterative Methods for Neutron Transport Eigenvalue Problems
We discuss iterative methods for computing criticality in nuclear reactors. In general this requires the solution of a generalised eigenvalue problem for an unsymmetric integro-differential operator in 6 independent variables, modelling transport, scattering and fission, where the dependent variable is the neutron angular flux. In engineering practice this problem is often solved iteratively, u...
متن کاملOn convergence of iterative projection methods for symmetric eigenvalue problems
We prove global convergence of particular iterative projection methods using the so-called shift-and-invert technique for solving symmetric generalized eigenvalue problems. In particular, we aim to provide a variant of the convergence theorem obtained by Crouzeix, Philippe, and Sadkane for the generalized Davidson method. Our result covers the Jacobi-Davidson and the rational Krylov methods wit...
متن کاملMixed Precision Iterative Refinement Techniques for the Solution of Dense Linear Systems
By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to exotic technologies such as Field Programmable Gate Arrays (FPGA), Graphical P...
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: Procedia Computer Science
سال: 2013
ISSN: 1877-0509
DOI: 10.1016/j.procs.2013.06.002