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877
Proximal thresholding algorithm for minimization over orthonormal bases
 SIAM Journal on Optimization
, 2007
"... The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convexanalytical tools, we extend this notion to that of proximal thresholding and inve ..."
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Cited by 62 (14 self)
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The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convexanalytical tools, we extend this notion to that of proximal thresholding
Random orthonormal bases of spaces of high dimension
, 1210
"... Abstract. We consider a sequence HN of finite dimensional Hilbert spaces of dimensions dN →∞. Motivating examples are eigenspaces, or spaces of quasimodes, for a Laplace or Schrödinger operator on a compact Riemannian manifold. The set of Hermitian orthonormal bases of HN may be identified with U( ..."
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Cited by 4 (0 self)
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Abstract. We consider a sequence HN of finite dimensional Hilbert spaces of dimensions dN →∞. Motivating examples are eigenspaces, or spaces of quasimodes, for a Laplace or Schrödinger operator on a compact Riemannian manifold. The set of Hermitian orthonormal bases of HN may be identified with U
POINTWISE BOUNDS FOR ORTHONORMAL BASIS ELEMENTS IN HILBERT SPACES
"... The following question is somewhat implicit in parts of [K1]: let Y be a nonempty finite set, let ν: Y →]0, 1] be a probability density on Y, i.e., a map such that ν(y) = 1, ..."
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The following question is somewhat implicit in parts of [K1]: let Y be a nonempty finite set, let ν: Y →]0, 1] be a probability density on Y, i.e., a map such that ν(y) = 1,
IDEAL NORMS AND TRIGONOMETRIC ORTHONORMAL SYSTEMS
, 1994
"... Abstract. In this article, we characterize the UMD–property of a Banach space X by ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of that numerical parameters can be used to decide whether or not X is a UMD–space. Moreover, in the negative case, we obtain a me ..."
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Abstract. In this article, we characterize the UMD–property of a Banach space X by ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of that numerical parameters can be used to decide whether or not X is a UMD–space. Moreover, in the negative case, we obtain a
MATLAB Programs for Generating Orthonormal Wavelets
"... Abstract: This paper presents MATLAB programs for generating the coefficients of the lowpass analysis filter corresponding to orthonormal wavelet analyses. One of the programs generates the famous Daubechies maxflat wavelets, and a second generates the Daubechies complex symmetric orthonormal wavel ..."
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wavelets. The remaining two programs generate the space of all orthonormal wavelets in terms of parameterizations whereby the space of wavelets of a given length 2N is generated by N parameters. This software should prove useful where it is desired to perform an optimization to obtain the best wavelet
Canonical orthonormal Wigner supermultiplet basis
, 1986
"... Abstract. The explicit construction of an orthonormal basis for states of good spin, isospin and SU(4) Wigner supermultiplet symmetry is given in a Bargmann representation space. A complete set of quantum labels is provided by a Sp(3,!HI 3 U ( 3) complementary symmetry. 1. ..."
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Abstract. The explicit construction of an orthonormal basis for states of good spin, isospin and SU(4) Wigner supermultiplet symmetry is given in a Bargmann representation space. A complete set of quantum labels is provided by a Sp(3,!HI 3 U ( 3) complementary symmetry. 1.
Uniformly bounded orthonormal polynomials on the sphere
"... Abstract Given any ε > 0, we construct an orthonormal system of n k uniformly bounded polynomials of degree at most k on the unit sphere in R m+1 where n k is bigger than 1 − ε times the dimension of the space of polynomials of degree at most k. Similarly we construct an orthonormal system of se ..."
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Abstract Given any ε > 0, we construct an orthonormal system of n k uniformly bounded polynomials of degree at most k on the unit sphere in R m+1 where n k is bigger than 1 − ε times the dimension of the space of polynomials of degree at most k. Similarly we construct an orthonormal system
Orthonormal StronglyConstrained Neural Learning
 Proc. of Int J. Conf. on Neural Networks
, 1998
"... In this paper a new class of nonconventional neural optimization algorithms called Orthonormal StronglyConstrained (SOC) is presented. Here the general problem of the iterative search of maxima or minima of objective functions under the constraint of orthonormality is dealt. After that general pro ..."
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Cited by 1 (1 self)
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In this paper a new class of nonconventional neural optimization algorithms called Orthonormal StronglyConstrained (SOC) is presented. Here the general problem of the iterative search of maxima or minima of objective functions under the constraint of orthonormality is dealt. After that general
General Existence Theorems For Orthonormal Wavelets, an abstract approach
 Publ. RIMS, Kyoto Univ
, 1995
"... APPROACH L. Baggett A. Carey W. Moran P. Ohring Abstract. Methods from noncommutative harmonic analysis are used to develop an abstract theory of orthonormal wavelets. The relationship between the existence of an orthonormal wavelet and the existence of a multiresolution is clarified, and four theo ..."
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Cited by 33 (2 self)
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APPROACH L. Baggett A. Carey W. Moran P. Ohring Abstract. Methods from noncommutative harmonic analysis are used to develop an abstract theory of orthonormal wavelets. The relationship between the existence of an orthonormal wavelet and the existence of a multiresolution is clarified, and four
Results 11  20
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877