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282,456
Spectral Theory
"... This chapter is devoted to the spectral theory of selfadjoint, differential operators. We cover a number of different topics, beginning in §1 with a proof of the spectral theorem. It was an arbitrary choice to put that material here, rather than in Appendix A, on functional analysis. The main ..."
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This chapter is devoted to the spectral theory of selfadjoint, differential operators. We cover a number of different topics, beginning in §1 with a proof of the spectral theorem. It was an arbitrary choice to put that material here, rather than in Appendix A, on functional analysis. The main
Spectral Theory of
"... This paper probes the spectral theory of the L 1 filtering / smoothing problem in the 2 block format. The solution for the filter/smoother which satisfies a L 1 performance bound, is presented. Using spectral properties of the problem, it is proved that extending our scope of acceptable compens ..."
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This paper probes the spectral theory of the L 1 filtering / smoothing problem in the 2 block format. The solution for the filter/smoother which satisfies a L 1 performance bound, is presented. Using spectral properties of the problem, it is proved that extending our scope of acceptable
Spectral Theory
, 2007
"... In many applications it is important to understand the spectral properties of a linear operator T: X → X, where X is some vector space over IR or IC. In the finite dimensional (complex) case linear operators may be characterised as matrices and the Jordan normal form theorem applies, providing a bas ..."
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basis of generalised eigenvectors. If, in addition, T is normal (i.e. T and T ∗ commute) with respect to an inner product, then the basis is orthogornal and consists of eigenvectors only. For spectral theory it is often convenient to work in complex spaces. For symmetric operators however the real
SPECTRAL THEORY OF ORTHOGONAL POLYNOMIALS
 WSPC PROCEEDINGS
, 2012
"... This is a summary of a talk given at ICMP 2012. It discusses some recent results in spectral theory through the prism of a newfound synergy between the spectral theory and OP communities. ..."
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This is a summary of a talk given at ICMP 2012. It discusses some recent results in spectral theory through the prism of a newfound synergy between the spectral theory and OP communities.
On Spectral Clustering: Analysis and an algorithm
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
, 2001
"... Despite many empirical successes of spectral clustering methods  algorithms that cluster points using eigenvectors of matrices derived from the distances between the points  there are several unresolved issues. First, there is a wide variety of algorithms that use the eigenvectors in slightly ..."
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Cited by 1697 (13 self)
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in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze
Algebraic Aspects of Spectral Theory
, 2010
"... We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of n × n matrices with entries that are polynomials or more general analytic functions. ..."
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We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of n × n matrices with entries that are polynomials or more general analytic functions.
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
 Advances in Neural Information Processing Systems 14
, 2001
"... Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher ..."
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Cited by 664 (8 self)
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Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered.
Spectral Theory of Thermal Relaxation
 J. Math. Phys
, 1997
"... . We review some results obtained in a recent series of papers on thermal relaxation in classical and quantum dissipative systems. We consider models where a small system S , with a finite number of degrees of freedom, interacts with a large environment R in thermal equilibrium at positive temperatu ..."
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Cited by 14 (1 self)
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with the Gibbs canonical ensemble associated with S . For simple models we prove that the above picture is correct, provided the equilibrium state of the environment R is itself given by its canonical ensemble. In the quantum case we also obtain an exact formula for the thermal relaxation time. Spectral Theory
Results 1  10
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282,456