Results 1  10
of
329,531
Blind Source Separation via Symmetric Eigenvalue Decomposition
 IN: PROCEEDING OF THE SIXTH INTERNATIONAL SYMPOSIUM ON SIGNAL PROCESSING AND ITS APPLICATIONS, KUALA LUMPUR
, 2001
"... We propose a new sufficient condition for separation of colored source signals with temporal structure, stating that the separation is possible, if the source signals have different higher selfcorrelation functions of even order. We show that the problem of blind source separation of uncorrelated c ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
colored signals can be converted to a symmetric eigenvalue problem of a special covariance matrix depending ondimensional parameter, if this matrix has distinct eigenvalues. We prove that the parameters for which this is possible, form an open subset of, which complement has a Lebesgue measure zero. We
STABLE AND EFFICIENT SPECTRAL DIVIDE AND CONQUER ALGORITHMS FOR THE SYMMETRIC EIGENVALUE DECOMPOSITION AND THE SVD
, 2012
"... Spectral divide and conquer algorithms solve the eigenvalue problem for all the eigenvalues and eigenvectors by recursively computing an invariant subspace for a subset of the spectrum and using it to decouple the problem into two smaller subproblems. A number of such algorithms have been develope ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
algorithms currently used. We present new spectral divide and conquer algorithms for the symmetric eigenvalue problem and the singular value decomposition that are backward stable, achieve lower bounds on communication costs recently derived by Ballard, Demmel, Holtz, and Schwartz, and have operation counts
A multilinear singular value decomposition
 SIAM J. Matrix Anal. Appl
, 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are ..."
Abstract

Cited by 470 (22 self)
 Add to MetaCart
., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pairwise symmetric tensors.
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 776 (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
The geometry of algorithms with orthogonality constraints
 SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
Abstract

Cited by 638 (1 self)
 Add to MetaCart
In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
Abstract

Cited by 990 (4 self)
 Add to MetaCart
. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums
The eigenvalues of random symmetric matrices
 Combinatorica
, 1981
"... Let A:(at;) be an zxn matrix whose entries for i=j are independent random variables and ai;:aii. Suppose that every a;; is bounded and for eveÍy i>j we have Eaii:!, D2ai,:62 and Eaiiv. E. P. Wigner determined the asymptotic behavior of the eigenvalues of I (semicircle law). In particular, for a ..."
Abstract

Cited by 179 (0 self)
 Add to MetaCart
Let A:(at;) be an zxn matrix whose entries for i=j are independent random variables and ai;:aii. Suppose that every a;; is bounded and for eveÍy i>j we have Eaii:!, D2ai,:62 and Eaiiv. E. P. Wigner determined the asymptotic behavior of the eigenvalues of I (semicircle law). In particular
Backward Errors for Eigenvalue and Singular Value Decompositions
, 1994
"... . We present bounds on the backward errors for the symmetric eigenvalue decomposition and the singular value decomposition in the twonorm and in the Frobenius norm. Through different orthogonal decompositions of the computed eigenvectors we can define different symmetric backward errors for the eig ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
. We present bounds on the backward errors for the symmetric eigenvalue decomposition and the singular value decomposition in the twonorm and in the Frobenius norm. Through different orthogonal decompositions of the computed eigenvectors we can define different symmetric backward errors
Eigenvalue
"... estimates for preconditioned saddle point matrices Owe Axelsson ∗ Maya Neytcheva † New eigenvalue bounds for symmetric matrices of saddle point form are derived and applied for preconditioned versions of the matrices. The preconditioners enable efficient iterative solution of the corresponding linea ..."
Abstract
 Add to MetaCart
estimates for preconditioned saddle point matrices Owe Axelsson ∗ Maya Neytcheva † New eigenvalue bounds for symmetric matrices of saddle point form are derived and applied for preconditioned versions of the matrices. The preconditioners enable efficient iterative solution of the corresponding
Results 1  10
of
329,531