Treffer: Open problems in computational linear algebra

Title:
Open problems in computational linear algebra
Authors:
SEN, S. K
Source:
Invited talks from the Fourth World Congress of Nonlinear Analysts (WCNA 2004), Orlando, florida, USA, 30 June-7 July 2004Nonlinear analysis. 63(5-7):926-934
Publisher Information:
Oxford: Elsevier, 2005.
Publication Year:
2005
Physical Description:
print, 28 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Géométrie algébrique, Algebraic geometry, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Algorithme déterministe, Deterministic algorithms, Algèbre linéaire, Linear algebra, Algebra lineal, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Calcul automatique, Computing, Cálculo automático, Complexité algorithme, Algorithm complexity, Complejidad algoritmo, Complexité calcul, Computational complexity, Complejidad computación, Erreur calcul, Computation error, Error cálculo, Grille, Grid, Rejilla, Maillage, Grid pattern, Celdarada, Mathématiques, Mathematics, Matemáticas, Modèle mathématique, Mathematical model, Modelo matemático, Multidisciplinaire, Multidisciplinary, Multidisciplinar, Multiplication, Multiplicación, Méthode optimisation, Optimization method, Método optimización, Nombre entier, Integer, Entero, Nombre réel, Real number, Número real, Plan expérience, Experimental design, Plan experiencia, Potentiel, Potential, Potencial, Problème non linéaire, Nonlinear problems, Résolution(math), Solving, Resolución (matemática), Solution bornée, Bounded solution, Solución acotada, Superficie, Area, Système linéaire, Linear system, Sistema lineal, Temps polynomial, Polynomial time, Tiempo polinomial, Test statistique, Statistical test, Test estadístico, Vérification, Verification, Verificación, 14C20, 15XX, 49XX, 65F05, 65Kxx, Algorithme itératif, Algorithme linéaire, Algorithme polynomial, Algorithme temps linéaire, Algèbre algorithmique, Optimisation non linéaire, Problème linéaire, Programme linéaire, Complexity, Computational linear algebra, Open problems, Optimization, Polynomial-time deterministic algorithm
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, United States
ISSN:
0362-546X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17350003
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.17350003
Database:
PASCAL Archive

Weitere Informationen

In the recent past a few important open problems such as those involving developing polynomial-time iterative algorithms for solving linear programs in both integer and real number models and for testing and generating primes have been solved. There are still several problems we have not found solutions over decades/centuries. Problems such as those involving (i) devising a deterministic noniterative polynomial-time algorithm for linear programs, (ii) deciding a priori all required fail-proof prime bases for errorfree computations for linear systems and linear optimization, (iii) determining computational complexities in some deterministic algorithms, (iv) designing algorithms with the lowest possible bound of complexity for matrix multiplications, (v) developing a polynomial-time deterministic algorithm for computing the error-bounds in an error-free computation, (vi) verification of the solution of some nonlinear optimization problems in polynomial time, (vii) obtaining the error-bounds in the solution of some linear/nonlinear problems when solved probabilistically are open problems. The solution of these open problems has the potential to revolutionize the whole area of computational mathematics and science as well as super-/grid-computing. We present here some of these open problems precisely along with the related discussions.