Results 1  10
of
3,435,319
Linear Equation Systems 1
"... Abstract There are several algorithms for solving linear system of equations. Iteration algorithms are recommended for the large linear systems with sparse matrix. But in the case of general n x m matrices, the classic iterative algorithms are not applicable with a few exceptions. So, In this pape ..."
Abstract
 Add to MetaCart
Abstract There are several algorithms for solving linear system of equations. Iteration algorithms are recommended for the large linear systems with sparse matrix. But in the case of general n x m matrices, the classic iterative algorithms are not applicable with a few exceptions. So
Definability of linear equation systems over groups and rings
"... Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and rings from the viewpoint of logical (inter)definability. A ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and rings from the viewpoint of logical (inter
{0, 1}Solutions of Integer Linear Equation Systems
 in Parallel Virtual Machine { EuroPVM'96
, 1996
"... A parallel version of an algorithm for solving systems of integer linear equations with {0, 1}variables is presented. The algorithm is based on lattice basis reduction in combination with explicit enumeration. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
A parallel version of an algorithm for solving systems of integer linear equations with {0, 1}variables is presented. The algorithm is based on lattice basis reduction in combination with explicit enumeration.
DEFINABILITY OF LINEAR EQUATION SYSTEMS OVER GROUPS AND RINGS
, 2013
"... Vol. 9(4:12)2013, pp. 1–26 www.lmcsonline.org ..."
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
Abstract

Cited by 649 (21 self)
 Add to MetaCart
gradient algorithms, indicating that I~QR is the most reliable algorithm when A is illconditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmationleast squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebralinear systems (direct and
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
Abstract

Cited by 766 (23 self)
 Add to MetaCart
illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract

Cited by 560 (10 self)
 Add to MetaCart
We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
Abstract

Cited by 1400 (17 self)
 Add to MetaCart
fraction of the output is corrupted. This work is related to the problem of finding sparse solutions to vastly underdetermined systems of linear equations. There are also significant connections with the problem of recovering signals from highly incomplete measurements. In fact, the results introduced
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
Abstract

Cited by 568 (23 self)
 Add to MetaCart
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding
New results in linear filtering and prediction theory
 Trans. ASME, Ser. D, J. Basic Eng
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
Abstract

Cited by 585 (0 self)
 Add to MetaCart
A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Results 1  10
of
3,435,319