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STOC
2012
ACM
242views Algorithms» more  STOC 2012»
6 years 9 months ago
Separating multilinear branching programs and formulas
This work deals with the power of linear algebra in the context of multilinear computation. By linear algebra we mean algebraic branching programs (ABPs) which are known to be com...
Zeev Dvir, Guillaume Malod, Sylvain Perifel, Amir ...
CALCO
2011
Springer
205views Mathematics» more  CALCO 2011»
7 years 7 months ago
Bases as Coalgebras
Abstract. The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of thi...
Bart Jacobs
SIAMSC
2010
141views more  SIAMSC 2010»
8 years 5 months ago
Blendenpik: Supercharging LAPACK's Least-Squares Solver
Abstract. Several innovative random-sampling and random-mixing techniques for solving problems in linear algebra have been proposed in the last decade, but they have not yet made a...
Haim Avron, Petar Maymounkov, Sivan Toledo
TOMS
2008
120views more  TOMS 2008»
8 years 7 months ago
Families of algorithms related to the inversion of a Symmetric Positive Definite matrix
We present families of algorithms for operations related to the computation of the inverse of a Symmetric Positive Definite (SPD) matrix: Cholesky factorization, inversion of a tr...
Paolo Bientinesi, Brian C. Gunter, Robert A. van d...
TC
2008
8 years 7 months ago
High-Performance Designs for Linear Algebra Operations on Reconfigurable Hardware
Numerical linear algebra operations are key primitives in scientific computing. Performance optimizations of such operations have been extensively investigated. With the rapid adva...
Ling Zhuo, Viktor K. Prasanna
COMBINATORICS
2007
85views more  COMBINATORICS 2007»
8 years 7 months ago
Eigenvectors and Reconstruction
In this paper, we study the simple eigenvectors of two hypomorphic matrices using linear algebra. We also give new proofs of results of Godsil and McKay.
Hongyu He
CSL
2010
Springer
8 years 8 months ago
Formal Theories for Linear Algebra
We introduce two-sorted theories in the style of [CN10] for the complexity classes L and DET, whose complete problems include determinants over Z2 and Z, respectively. We then desc...
Stephen Cook, Lila Fontes
PPSC
1989
8 years 8 months ago
Evaluating Block Algorithm Variants in LAPACK
The LAPACK software project currently under development is intended to provide a portable linear algebra library for high performance computers. LAPACK will make use of the Level 1...
Ed Anderson, Jack Dongarra
WSC
2007
8 years 9 months ago
Duality in high level petri-nets: a basis to do diagnoses
In this paper the relation of high-level Petri-nets (hlpn) and linear algebra is outlined. On the basis of this relation the theory of the dual spaces can be brought in to a new c...
Jörg R. Müller, Eckehard Schnieder
PARA
1995
Springer
8 years 10 months ago
ScaLAPACK Tutorial
Abstract. ScaLAPACK is a library of high performance linear algebra routines for distributed memory MIMD computers. It is a continuation of the LAPACK project, which designed and p...
Jack Dongarra, Antoine Petitet
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