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632
The Sparse Eigenvalue Problem
 In arXiv:0901.1504v1
, 2009
"... In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA), ..."
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In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA
Truncated Power Method for Sparse Eigenvalue Problems
"... This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most k nonzero components. We propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem. A st ..."
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Cited by 32 (1 self)
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This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most k nonzero components. We propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem. A
Sparse Regression as a Sparse Eigenvalue Problem
"... Abstract — We extend the l0norm “subspectral ” algorithms developed for sparseLDA [5] and sparsePCA [6] to more general quadratic costs such as MSE in linear (or kernel) regression. The resulting ”Sparse Least Squares ” (SLS) problem is also NPhard, by way of its equivalence to a rank1 sparse e ..."
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Cited by 10 (1 self)
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Abstract — We extend the l0norm “subspectral ” algorithms developed for sparseLDA [5] and sparsePCA [6] to more general quadratic costs such as MSE in linear (or kernel) regression. The resulting ”Sparse Least Squares ” (SLS) problem is also NPhard, by way of its equivalence to a rank1 sparse
An Implementation and Evaluation of the AMLS Method for Sparse Eigenvalue Problems
"... We describe an efficient implementation and present a performance study of an Algebraic MultiLevel Substructuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the algorithm, and compare it with the shiftandinvert Lanczo ..."
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Cited by 12 (2 self)
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We describe an efficient implementation and present a performance study of an Algebraic MultiLevel Substructuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the algorithm, and compare it with the shift
A DC Programming Approach for Sparse Eigenvalue Problem
"... We investigate the sparse eigenvalue problem which arises in various fields such as machine learning and statistics. Unlike standard approaches relying on approximation of the l0norm, we work with an equivalent reformulation of the problem at hand as a DC program. Our starting point is the eigenvalu ..."
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We investigate the sparse eigenvalue problem which arises in various fields such as machine learning and statistics. Unlike standard approaches relying on approximation of the l0norm, we work with an equivalent reformulation of the problem at hand as a DC program. Our starting point
Projection methods for nonlinear sparse eigenvalue problems
, 2005
"... Abstract. This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynom ..."
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Cited by 2 (0 self)
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Abstract. This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature
Solving large sparse eigenvalue problems on supercomputers
 IN PROCEEDINGS OF INTERNATIONAL WORKSHOP ON PARALLEL ALGORITHMS AND ARCHITECTURES
"... An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is t ..."
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An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods
Reducing Synchronization on the Parallel Davidson method for the Large, Sparse, Eigenvalue Problem
 In Supercomputing '93
, 1993
"... The Davidson method is extensively used in quantum chemistry and atomic physics for finding a few extreme eigenpairs of a large, sparse, symmetric matrix. It can be viewed as a preconditioned version of the Lanczos method which reduces the number of iterations at the expense of a more complicated st ..."
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Cited by 8 (6 self)
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The Davidson method is extensively used in quantum chemistry and atomic physics for finding a few extreme eigenpairs of a large, sparse, symmetric matrix. It can be viewed as a preconditioned version of the Lanczos method which reduces the number of iterations at the expense of a more complicated
Efficient Solution Of Large Sparse Eigenvalue Problems In Microelectronic Simulation
 Prvc. of the Cornelius Lanczos Int. Centenary
, 1993
"... CONTENTS CHAPTER PAGE 1 INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 EFFICIENT NUMERICAL SIMULATION OF ELECTRON STATES IN QUANTUM WIRES : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : ..."
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: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 The equations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.3 Reformulation as a fixed point problem : : : : : : : : : : : : : : : : : : : 13 2.4 The Eigenvalue Problem for Schrodinger's Equation : : : : : : : : : : : : 16 2.5 The Solution of the Nonlinear Poisson
Methods for Large Sparse Eigenvalue Problems from Waveguide Analysis
"... We discuss several techniques for finding leading eigenvalues and eigenvectors for large sparse matrices. The techniques are demonstrated on a scalar Helmholtz equation derived from a model semiconductor rib waveguide problem. We compare the simple inverse iteration approach with more sophisticated ..."
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We discuss several techniques for finding leading eigenvalues and eigenvectors for large sparse matrices. The techniques are demonstrated on a scalar Helmholtz equation derived from a model semiconductor rib waveguide problem. We compare the simple inverse iteration approach with more sophisticated
Results 1  10
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