SHORT-SS4: Error-Free Transformation of Matrix Multiplication by A Posteriori Verification
نویسندگان
چکیده
This paper is concerned with accurate computations for matrix multiplication. An error-free transformation of matrix multiplication is developed by the authors. It transforms a product of two floatingpoint matrices to a sum of several floating-point matrices by using only floating-point arithmetic. This transformation is useful not only for accurate matrix multiplication but also for interval enclosures of matrix products. The key technique is an error-free splitting of floating-point numbers. We improve known error-free splitting and develop an a posteriori validation method for the error-free transformation.
منابع مشابه
Equivalent a posteriori error estimates for spectral element solutions of constrained optimal control problem in one dimension
In this paper, we study spectral element approximation for a constrained optimal control problem in one dimension. The equivalent a posteriori error estimators are derived for the control, the state and the adjoint state approximation. Such estimators can be used to construct adaptive spectral elements for the control problems.
متن کاملA New Parallel Matrix Multiplication Method Adapted on Fibonacci Hypercube Structure
The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...
متن کاملMultiplierless Dct Algorithm for Image Compression Applications
Abstract: This paper presents a novel error-free (infinite-precision) architecture for the fast implementation of 8x8 2-D Discrete Cosine Transform. The architecture uses a new algebraic integer encoding of a 1-D radix-8 DCT that allows the separable computation of a 2-D 8x8 DCT without any intermediate number representation conversions. This is a considerable improvement on previously introduc...
متن کاملAlgebraic adjoint of the polynomials-polynomial matrix multiplication
This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field
متن کاملA posteriori $ L^2(L^2)$-error estimates with the new version of streamline diffusion method for the wave equation
In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.
متن کامل