Results 1 - 10 of 5,899

Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization

by Farid Alizadeh - SIAM Journal on Optimization , 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
Abstract - Cited by 547 (12 self) - Add to MetaCart
We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized

Stochastic Perturbation Theory

by G. W. Stewart , 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a first-order perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
Abstract - Cited by 907 (36 self) - Add to MetaCart
and the eigenvalue problem. Key words. perturbation theory, random matrix, linear system, least squares, eigenvalue, eigenvector, invariant subspace, singular value AMS(MOS) subject classifications. 15A06, 15A12, 15A18, 15A52, 15A60 1. Introduction. Let A be a matrix and let F be a matrix valued function of A

LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares

by Christopher C. Paige, Michael A. Saunders - 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 653 (21 self) - Add to MetaCart
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

For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1-norm Solution is also the Sparsest Solution

by David L. Donoho - 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 568 (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

The Dantzig selector: statistical estimation when p is much larger than n

by Emmanuel Candes, Terence Tao , 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
Abstract - Cited by 879 (14 self) - Add to MetaCart
In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n

Hierarchical Modelling and Analysis for Spatial Data. Chapman and Hall/CRC,

by S Banerjee , B P Carlin , A E Gelfand , Chapman , / Hall , New Crc , N York; Cressie , P J Diggle , P J Ribeiro Jr , B D Ripley , 2004
"... Abstract Often, there are two streams in statistical research -one developed by practitioners and other by main stream statisticians. Development of geostatistics is a very good example where pioneering work under realistic assumptions came from mining engineers whereas it is only now that statisti ..."
Abstract - Cited by 442 (45 self) - Add to MetaCart
that statistical framework is getting more transparent. The subject with statistical emphasis has been evolving, as seen by various excellent books from statistical sides (Banerjee, S., Introduction It is well known that the maximum likelihood (ML) method is a powerful statistical tool in estimation

ANISOTROPY OF MAGNETIC SUSCEPTIBILITY STUDY OF KAOLINITE MATRIX SUBJECTED TO BIAXIAL TESTS

by Aniruddha Sengupta
"... Abstract—The potential for structural failure of consolidated clay materials, which is of great importance in many applications, typically are assessed by measuring the localized strain bands that develop under anisotropic load stress. Most methods are precluded from providing a full understanding o ..."
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of the strain anisotropy because they only give two-dimensional information about the stressed clay blocks. The purpose of the present study was to investigate three-dimensional strain localization in a kaolinite matrix, caused by strain anisotropy due to a biaxial plane-strain test, using a relatively new

Matrix Completion with Noise

by Emmanuel J. Candès, Yaniv Plan
"... On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest ..."
Abstract - Cited by 255 (13 self) - Add to MetaCart
completion, which shows that under some suitable conditions, one can recover an unknown low-rank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclear-norm minimization subject to data constraints. Further, this paper introduces novel results showing

DETERMINANT MAXIMIZATION WITH LINEAR MATRIX INEQUALITY CONSTRAINTS

by Lieven Vandenberghe , Stephen Boyd , Shao-po Wu
"... The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the s ..."
Abstract - Cited by 223 (18 self) - Add to MetaCart
The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization

Users' Guide for the Harwell-Boeing Sparse Matrix Collection (Release I)

by Iain S. Duff, Roger G. Grimes, John G. Lewis , 1992
"... We describe the complete set of matrices in the Harwell-Boeing sparse matrix collection, a set of standard test matrices for sparse matrix problems. This description includes some documentation for each matrix (or set of matrices) in the collection. We also describe how a copy of the collection may ..."
Abstract - Cited by 265 (23 self) - Add to MetaCart
be obtained. Keywords: sparse matrices, test matrices, matrix collection AMS(MOS) subject classifications: 65F50, 65F05, 65F15, 65F20. 1 Current reports available by anonymous ftp from matisa.cc.rl.ac.uk in the directory "pub/reports". This report is in file duglRAL92086.ps.gz. Also published
Results 1 - 10 of 5,899