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An analysis of the RayleighRitz method for approximating eigenspaces
 Math. Comp
, 1999
"... Abstract. This paper concerns the Rayleigh–Ritz method for computing an approximation to an eigenspace X of a general matrix A from a subspace W that contains an approximation to X. The method produces a pair (N, ˜ X) that purports to approximate a pair (L, X), where X is a basis for X and AX = XL. ..."
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Cited by 28 (10 self)
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Abstract. This paper concerns the Rayleigh–Ritz method for computing an approximation to an eigenspace X of a general matrix A from a subspace W that contains an approximation to X. The method produces a pair (N, ˜ X) that purports to approximate a pair (L, X), where X is a basis for X and AX = XL
RayleighRitz Approximation and Refinement of Periodic Matrix Pairs
"... In this paper, we study the RayleighRitz approximation for the eigenproblem of periodic matrix pairs. We show the convergence of the Ritz value and periodic Ritz vectors. Furthermore, we prove the convergence of refined periodic Ritz vectors and propose an efficient algorithm for computing the refi ..."
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In this paper, we study the RayleighRitz approximation for the eigenproblem of periodic matrix pairs. We show the convergence of the Ritz value and periodic Ritz vectors. Furthermore, we prove the convergence of refined periodic Ritz vectors and propose an efficient algorithm for computing
RayleighRitz approximation for the linear response eigenvalue problem
, 2013
"... Large scale eigenvalue computation is about approximating certain invariant subspaces associated with the interested part of the spectrum, and the interested eigenvalues are then extracted from projecting the problem by approximate invariant subspaces into a much smaller eigenvalue problem. In th ..."
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Cited by 1 (1 self)
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on the canonical angles in terms of eigenvalue approximation errors. They are useful in analyzing numerical solutions to linear response eigenvalue problems. Key words. Linear response eigenvalue problem, eigenvalue approximation, RayleighRitz
QUADRATIC INTERPOLATION AND RAYLEIGHRITZ METHODS FOR BIFURCATION COEFFICIENTS ∗
, 903
"... Abstract. In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of RayleighRitz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations converge in a norm of sufficient strength to rend ..."
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Abstract. In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of RayleighRitz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations converge in a norm of sufficient strength
ViewBased and Modular Eigenspaces for Face Recognition
 IEEE INTERNATIONAL CONFERENCE ON COMPUTER VISION & PATTERN RECOGNITION
, 1994
"... In this work we describe experiments with eigenfaces for recognition and interactive search in a largescale face database. Accurate visual recognition is demonstrated using a database of o(10^3) faces. The problem of recognition under general viewing orientation is also explained. A viewbased mul ..."
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Cited by 770 (15 self)
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based multipleobserver eigenspace technique is proposed for use in face recognition under variable pose. In addition, a modular eigenspace description technique is used which incorporates salient features such as the eyes, nose, mouth, in a eigenfeature layer. This modular representation yields higher
Generalizations of harmonic and refined Rayleigh–Ritz
, 2004
"... Abstract. We investigate several generalizations of the harmonic and refined Rayleigh–Ritz method. These may be practical when one is interested in eigenvalues close to one of two targets (for instance, when the eigenproblem has Hamiltonian structure such that eigenvalues come in pairs or quadruples ..."
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Cited by 2 (1 self)
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Abstract. We investigate several generalizations of the harmonic and refined Rayleigh–Ritz method. These may be practical when one is interested in eigenvalues close to one of two targets (for instance, when the eigenproblem has Hamiltonian structure such that eigenvalues come in pairs
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a
On RayleighRitz Method in ThreeParameter Eigenvalue Problems
"... This paper deals with the computation of the eigenvalues of a threeparameter SturmLiouville problem in the form of ordinary differential equation using RayleighRitz Method, a method which is based on the principle of variational methods. This method has been effective in computing the eigenvalues ..."
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the eigenvalues of selfadjoint problems. The resulting equations obtained in applying RayleighRitz method on the problem are solved to find the rough estimates of the eigenvalues of the problem. Rough estimates are used as starting approximations in the corresponding shooting method to obtain their actual
RAYLEIGHRITZ MAJORIZATION ERROR BOUNDS WITH APPLICATIONS TO FEM AND SUBSPACE ITERATIONS
, 2008
"... The RayleighRitz method finds the stationary values, called Ritz values, of the Rayleigh quotient on a given trial subspace as approximations to eigenvalues of a Hermitian operator A. If the trial subspace is Ainvariant, the Ritz values are exactly some of the eigenvalues of A. Given two subspace ..."
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Cited by 8 (4 self)
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The RayleighRitz method finds the stationary values, called Ritz values, of the Rayleigh quotient on a given trial subspace as approximations to eigenvalues of a Hermitian operator A. If the trial subspace is Ainvariant, the Ritz values are exactly some of the eigenvalues of A. Given two
Results 1  10
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