Result: Refining and verifying the solution of a linear system

Title:
Refining and verifying the solution of a linear system
Authors:
Nguyen, Hong Diep, Revol, Nathalie
Contributors:
Computer arithmetic (ARENAIRE), Centre Inria de l'Université Grenoble Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon), Université de Lyon-Centre National de la Recherche Scientifique (CNRS), ACM Digital Library
Source:
SNC 2011 - Symbolic Numeric Computation, Jun 2011, San Jose, United States
Publisher Information:
CCSD, 2011.
Publication Year:
2011
Collection:
collection:ENS-LYON
collection:CNRS
collection:INRIA
collection:UNIV-LYON1
collection:INRIA-RHA
collection:LIP
collection:INRIA_TEST
collection:TESTALAIN1
collection:INRIA2
collection:INRIA-RENGRE
collection:INRIA-300009
collection:UDL
collection:UNIV-LYON
Subject Terms:
accuracy, precision, floating-point arithmetic, interval arithmetic, symbolic-numeric, verified computations, numerical linear algebra, scientific computing, ACM: G.: Mathematics of Computing, G.1: NUMERICAL ANALYSIS, G.1.3: Numerical Linear Algebra, G.1.3.4: Linear systems (direct and iterative methods), G.1.3.3: Error analysis, [INFO.INFO-AO]Computer Science [cs], Computer Arithmetic
Subject Geographic:
San Jose, United States
Original Identifier:
HAL: hal-00641659
Document Type:
Conference conferenceObject<br />Conference papers
Language:
English
Access URL:
https://inria.hal.science/hal-00641659
https://inria.hal.science/hal-00641659v1/document
https://inria.hal.science/hal-00641659v1/file/Nguyen-Revol-SNC.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.00641659v1
Database:
HAL

Further Information

The problem considered here is to refine an approximate, numerical, solution of a linear system and simultaneously give an enclosure of the error between this approximate solution and the exact one: this is the verification step. Desirable properties for an algorithm solving this problem are accuracy of the results, complexity and performance of the actual implementation. A new algorithm is given, which has been designed with these desirable properties in mind. It is based on iterative refinement for accuracy, with well-chosen computing precisions, and uses interval arithmetic for verification.