Endmember extraction is a process to identify the spectra of materials from the hyperspectral scene. This paper presents a framework for endmember extraction by exploiting the ideas that: the endmembers are the vertic...
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(纸本)9781457710056
Endmember extraction is a process to identify the spectra of materials from the hyperspectral scene. This paper presents a framework for endmember extraction by exploiting the ideas that: the endmembers are the vertices of the simplex, and the calculation of simplex volume can be simplified by triangular factorization. triangular factorization is a broad conception including many methods, so the proposed framework is a group of methods including different implementations. Experimental results on both synthetic and real hyperspectral data demonstrate that the proposed algorithm can obtain the results with better accuracy and much lower complexity, comparing to other state-of-the-art approaches.
We recast Stahl’s counterexample from the point of view of the spectral theory of the underlying non-symmetric Jacobi matrices. In particular, it is shown that these matrices are self-adjoint and non-negativ...
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We recast Stahl’s counterexample from the point of view of the spectral theory of the underlying non-symmetric Jacobi matrices. In particular, it is shown that these matrices are self-adjoint and non-negative in a Krein space and have empty resolvent sets. In fact, the technique of Darboux transformations (aka commutation methods) on spectra which is used in the present paper allows us to treat the class of all GG-non-negative tridiagonal matrices. We also establish a correspondence between this class of matrices and the class of signed measures with one sign change. Finally, it is proved that the absence of the spurious pole at infinity for Padé approximants is equivalent to the definitizability of the corresponding tridiagonal matrix.
This paper proposes a novel direct reanalysis algorithm based on finding updated triangular factorization in sparse matrix solution. The key concept lies on the binary tree characteristics of the global stiffness matr...
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This paper proposes a novel direct reanalysis algorithm based on finding updated triangular factorization in sparse matrix solution. The key concept lies on the binary tree characteristics of the global stiffness matrix derived by a graph partitioner as fill-ins' reducer. Accommodating a local modification, the update of the triangular factor happens only, through a particular path of the binary tree, which traces back from modified nodes to the root node. Numerical examples show that the proposed algorithm improves reanalysis efficiency significantly, especially for high-rank structural modification. In terms of implementation, little additional storage is needed to perform the proposed algorithm. This method can be applied to a wide range of engineering problems and can be the foundation of a lot of subsequent analyses. (C) 2014 Elsevier Ltd. All rights reserved.
Unitriangular factorization is a presentation of a linear group as a product of unipotent radicals of a Borel subgroup and its opposite. Whether this decomposition is known for Chevalley groups over rings of stable ra...
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Unitriangular factorization is a presentation of a linear group as a product of unipotent radicals of a Borel subgroup and its opposite. Whether this decomposition is known for Chevalley groups over rings of stable rank 1 and some Dedekind rings of arithmetic type, the case of twisted groups has been studied only over finite fields. In the present paper we give a much simpler proof for twisted groups over finite fields and the field of complex numbers.
By a Hermite interpolation sequence we mean a sequence of Hermite interpolation polynomials of degree 0, 1,... such that consecutive terms satisfy the differentiation conditions of the previous ones. We extend this co...
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By a Hermite interpolation sequence we mean a sequence of Hermite interpolation polynomials of degree 0, 1,... such that consecutive terms satisfy the differentiation conditions of the previous ones. We extend this concept to arbitrary fields from the reals by purely algebraic means based on the possibility of formal Taylor expansions of rational fractions around any point of the underlying field. As an application we obtain recursion-free on-free explicit formulas for the entries of triangular decompositions of generalized Hermite-Vandermonde matrices. (C) 2013 Elsevier Inc. All rights reserved.
Let d mu be a probability measure on [0, +infinity) such that its moments are finite. Then the Cauchy-Stieltjes transform S of d mu is a Stieltjes function, which admits an expansion into a Stieltjes continued fractio...
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Let d mu be a probability measure on [0, +infinity) such that its moments are finite. Then the Cauchy-Stieltjes transform S of d mu is a Stieltjes function, which admits an expansion into a Stieltjes continued fraction. In the present paper, we consider a matrix interpretation of the unwrapping transformation S(lambda) bar right arrow lambda S(lambda(2)), which is intimately related to the simplest case of polynomial mappings. More precisely, it is shown that this transformation is essentially a Darboux transformation of the underlying Jacobi matrix. Moreover, in this scheme, the Chihara construction of solutions to the Carlitz problem appears as a shifted Darboux transformation. (C) 2013 Elsevier Inc. All rights reserved.
LetJ be a monic Jacobi matrix associated with the Cauchy transform F of a probability measure. We construct a pair of the lower and upper triangular block matrices L and U such thatJ = LU and the matrix 3c = UL is a m...
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LetJ be a monic Jacobi matrix associated with the Cauchy transform F of a probability measure. We construct a pair of the lower and upper triangular block matrices L and U such thatJ = LU and the matrix 3c = UL is a monic generalized Jacobi matrix associated with the function 3c (lambda) = lambda F(lambda) + 1. It turns out that the Christoffel transformation 3c of a bounded monic Jacobi matrixJ can be unbounded. This phenomenon is shown to be related to the effect of accumulating at infinity of the poles of the Pade approximants of the function 3c although 3c is holomorphic at infinity. The case of the UL-factorization ofJ is considered as well. (C) 2011 Elsevier Inc. All rights reserved.
Earlier, the Krein differential system has been studied under certain regularity conditions. In this paper, some cases are treated where these conditions are not fulfilled. Examples related to random matrix theory are...
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Earlier, the Krein differential system has been studied under certain regularity conditions. In this paper, some cases are treated where these conditions are not fulfilled. Examples related to random matrix theory are studied.
We introduce and investigate special classes of generalized stationary processes: white-noise-type processes and power-low processes. Operators which generate white-noise-type processes are interesting, in particular,...
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We introduce and investigate special classes of generalized stationary processes: white-noise-type processes and power-low processes. Operators which generate white-noise-type processes are interesting, in particular, because of their importance to random matrix theory, triangular factorization of operators and spectral theory.
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