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Cooperative strategies and capacity theorems for relay networks
 IEEE TRANS. INFORM. THEORY
, 2005
"... Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decodeandforward the source message to the destination, or they compressandforward their channel outputs to the destination. The decodeandforward scheme is a variant of ..."
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Cited by 737 (19 self)
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with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, singlebounce fading, certain quasistatic fading problems, cases where partial
Rayleigh quotient
, 2009
"... A ∈ Rm×m is symmetric if AT = A All eigenvalues of A λ1,...,λm are real A is unitarily diagonalizable — A has a set of m linearly independent orthonormal vectors q1,..., qm Eigenvectors are normalized ‖qj ‖ = 1, and sometimes the eigenvalues are ordered in a particular way Initial reduction to trid ..."
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A ∈ Rm×m is symmetric if AT = A All eigenvalues of A λ1,...,λm are real A is unitarily diagonalizable — A has a set of m linearly independent orthonormal vectors q1,..., qm Eigenvectors are normalized ‖qj ‖ = 1, and sometimes the eigenvalues are ordered in a particular way Initial reduction to tridiagonal form is assumed
On eigenvalues of a Rayleigh quotient matrix
 Linear Algebra Appl
, 1992
"... This note deals with the following problem: Let A be an n X n Hermitian matrix, and Q and 0 be two n X rn (n> m> 1) matrices both with orthonormal column vectors. How do the eigenvalues of the m X m Hermitian matrix Q”AQ differ from those of the m X m Hermitian matrix QHAQ? We give a positive ..."
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Cited by 3 (2 self)
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answer to one of the unsolved problems raised recently by Sun. In what follows, we will consider the following interesting problem concerning the spectral variation of a Rayleigh quotient matrix: Let A be an n X n Hermitian matrix, and Q and Q be two n X m (n> m> 1) matrices both with orthonormal
Rayleigh Quotient Based Optimization Methods For Eigenvalue Problems
, 2014
"... Four classes of eigenvalue problems that admit similar minmax principles and the Cauchy interlacing inequalities as the symmetric eigenvalue problem famously does are investigated. These minmax principles pave ways for efficient numerical solutions for extreme eigenpairs by optimizing the socalle ..."
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Cited by 1 (0 self)
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called Rayleigh quotient functions. In fact, scientists and engineers have already been doing that for computing the eigenvalues and eigenvectors of Hermitian matrix pencils A − λB with B positive definite, the first class of our eigenvalue problems. But little attention has gone to the other three classes
Alternatives To The Rayleigh Quotient For The Quadratic Eigenvalue Problem
 SIAM J. Sc. Comp
, 2001
"... We consider the quadratic eigenvalue problem 2 Ax + Bx + Cx = 0: Suppose that u is an approximation to an eigenvector x (for instance obtained by a subspace method), and that we want to determine an approximation to the corresponding eigenvalue . The usual approach is to impose the Galerkin condi ..."
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Cited by 2 (0 self)
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We consider the quadratic eigenvalue problem 2 Ax + Bx + Cx = 0: Suppose that u is an approximation to an eigenvector x (for instance obtained by a subspace method), and that we want to determine an approximation to the corresponding eigenvalue . The usual approach is to impose the Galerkin
Grassmannian beamforming for multipleinput multipleoutput wireless systems
 IEEE TRANS. INFORM. THEORY
, 2003
"... Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multipleinput and multipleoutput (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamformi ..."
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Cited by 329 (38 self)
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the distribution of the optimal beamforming vector in independent identically distributed Rayleigh fading matrix channels, the codebook design problem is solved and related to the problem of Grassmannian line packing. The proposed design criterion is flexible enough to allow for side constraints on the codebook
The continuoustime Rayleigh quotient flow on the Grassmann manifold
 Linear Algebra Appl
"... An extension of the Rayleigh quotient iteration (RQI) to the Grassmann manifold has been recently proposed for computing a pdimensional eigenspace of a symmetric matrix A. Here we analyze a continuoustime flow analogous to this Grassmannian RQI. This flow achieves deflation in finite time, i.e. ..."
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Cited by 4 (3 self)
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An extension of the Rayleigh quotient iteration (RQI) to the Grassmann manifold has been recently proposed for computing a pdimensional eigenspace of a symmetric matrix A. Here we analyze a continuoustime flow analogous to this Grassmannian RQI. This flow achieves deflation in finite time, i
Adjusting the Rayleigh Quotient in Semiorthogonal Lanczos Methods
, 2001
"... In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon [4] shows that the Rayleigh quotient  i.e., the tridiagonal matrix pr ..."
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Cited by 4 (0 self)
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In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon [4] shows that the Rayleigh quotient  i.e., the tridiagonal matrix
Results 1  10
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177,198