Add to ORKGWe give a concise summary of conditions for the convergence of iterative refinement and GMRES-based iterative refinement in three precisions, as well as the limiting forward errors and backward errors. All combinations of precisions of practical interest are included. As well as known results, we include new results for GMRES-based iterative refinement with the preconditioner applied at the working precision and the residual computed at the working precision
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear al...
Abstract. In hardware-aware high performance computing, block- asynchronous iteration and mixed prec...
We consider the solution of a linear system of equations using the GMRES iterative method. In [3], a...
We propose a general algorithm for solving a $n\times n$ nonsingular linear system $Ax = b$ based on...
We describe how variable precision floating-point arithmetic can be used to compute inner products i...
We present the design and testing of an algorithm for iterative refinement of the solution of linear...
summary:With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refine...
The technique of iterative refinement for improving the computed solution to a linear system was use...
Abstract. Consideration of an abstract improvement algorithm leads to the following principle, which...
Iterative refinement is a long-standing technique for improving the accuracy of a computed solution ...
The main purpose of this paper is the derivation of computable bounds on the residual norms of (full...
The increasing availability of very low precisions (tfloat32, fp16, bfloat16, fp8) in hardware pushe...
AbstractThe behavior of iterative methods of GMRES-type when applied to singular, possibly inconsist...
With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative ...
In this paper we show how the properties of integral operators and their approximations are reflecte...
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear al...
Abstract. In hardware-aware high performance computing, block- asynchronous iteration and mixed prec...
We consider the solution of a linear system of equations using the GMRES iterative method. In [3], a...
We propose a general algorithm for solving a $n\times n$ nonsingular linear system $Ax = b$ based on...
We describe how variable precision floating-point arithmetic can be used to compute inner products i...
We present the design and testing of an algorithm for iterative refinement of the solution of linear...
summary:With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refine...
The technique of iterative refinement for improving the computed solution to a linear system was use...
Abstract. Consideration of an abstract improvement algorithm leads to the following principle, which...
Iterative refinement is a long-standing technique for improving the accuracy of a computed solution ...
The main purpose of this paper is the derivation of computable bounds on the residual norms of (full...
The increasing availability of very low precisions (tfloat32, fp16, bfloat16, fp8) in hardware pushe...
AbstractThe behavior of iterative methods of GMRES-type when applied to singular, possibly inconsist...
With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative ...
In this paper we show how the properties of integral operators and their approximations are reflecte...
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear al...
Abstract. In hardware-aware high performance computing, block- asynchronous iteration and mixed prec...
We consider the solution of a linear system of equations using the GMRES iterative method. In [3], a...