The Experts below are selected from a list of 11463 Experts worldwide ranked by ideXlab platform
Laura Rebollo-neira - One of the best experts on this subject based on the ideXlab platform.
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Fast communication: Sparse signal representation by adaptive non-uniform B-spline dictionaries on a Compact Interval
Signal Processing, 2010Co-Authors: Laura Rebollo-neira, Zhiqiang XuAbstract:Non-uniform B-spline dictionaries on a Compact Interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B-spline functions of broader support than those corresponding to the B-spline basis for the identical space. Such dictionaries are meant to assist in the construction of adaptive sparse signal representation through a combination of stepwise optimal greedy techniques.
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Adaptive non-uniform B-spline dictionaries on a Compact Interval
arXiv: Functional Analysis, 2009Co-Authors: Laura Rebollo-neiraAbstract:Non-uniform B-spline dictionaries on a Compact Interval are discussed. For each given partition, dictionaries of B-spline functions for the corresponding spline space are constructed. It is asserted that, by dividing the given partition into subpartitions and joining together the bases for the concomitant subspaces, slightly redundant dictionaries of B-splines functions are obtained. Such dictionaries are proved to span the spline space associated to the given partition. The proposed construction is shown to be potentially useful for the purpose of sparse signal representation. With that goal in mind, spline spaces specially adapted to produce a sparse representation of a given signal are considered.
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Cardinal B-spline dictionaries on a Compact Interval
Applied and Computational Harmonic Analysis, 2005Co-Authors: Miroslav Andrle, Laura Rebollo-neiraAbstract:Abstract A prescription for constructing dictionaries for cardinal spline spaces on a Compact Interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a Compact Interval can be spanned by dictionaries of cardinal B-spline functions of broader support than the corresponding basis functions.
Zhiqiang Xu - One of the best experts on this subject based on the ideXlab platform.
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Fast communication: Sparse signal representation by adaptive non-uniform B-spline dictionaries on a Compact Interval
Signal Processing, 2010Co-Authors: Laura Rebollo-neira, Zhiqiang XuAbstract:Non-uniform B-spline dictionaries on a Compact Interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B-spline functions of broader support than those corresponding to the B-spline basis for the identical space. Such dictionaries are meant to assist in the construction of adaptive sparse signal representation through a combination of stepwise optimal greedy techniques.
Holger Dette - One of the best experts on this subject based on the ideXlab platform.
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A note on some random orthogonal polynomials on a Compact Interval
Proceedings of the American Mathematical Society, 2009Co-Authors: Melanie Birke, Holger DetteAbstract:We consider a uniform distribution on the setMk of moments of order k2 N corresponding to probability measures on the Interval [0;1]. To each (random) vector of moments inM2n 1 we consider the corresponding uniquely determined monic (random) orthogonal polynomial of degree n and study the asymptotic properties of its roots if n!1.
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A note on random orthogonal polynomials on a Compact Interval
arXiv: Probability, 2008Co-Authors: Melanie Birke, Holger DetteAbstract:We consider a uniform distribution on the set $\mathcal{M}_k$ of moments of order $k \in \mathbb{N}$ corresponding to probability measures on the Interval $[0,1]$. To each (random) vector of moments in $\mathcal{M}_{2n-1}$ we consider the corresponding uniquely determined monic (random) orthogonal polynomial of degree $n$ and study the asymptotic properties of its roots if $n \to \infty$.
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Quadrature formulas for matrix measures—a geometric approach
Linear Algebra and its Applications, 2003Co-Authors: Holger Dette, William J. StuddenAbstract:A geometric approach to quadrature formulas for matrix measures is presented using the relations between the representations of the boundary points of the moment space (generated by all matrix measures) and quadrature formulas. Simple proofs of existence and uniqueness of quadrature formulas of maximal degree of precision are given. Several new quadrature formulas for matrix measures supported on a Compact Interval are presented and several examples are discussed. Additionally, a special construction of degenerated quadrature formulas is discussed and some results regarding the location of the zeros of polynomials orthogonal with respect to a matrix measure on a Compact Interval are obtained as a by-product.
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New Identities for Orthogonal Polynomials on a Compact Interval
Journal of Mathematical Analysis and Applications, 1993Co-Authors: Holger DetteAbstract:Abstract We derive new identities for orthonormal polynomials with respect to an arbitrary (probability) measure on the Interval [−1, 1], which generalize the well known identity (1 − x 2 ) U 2 n −1 ( x ) + T 2 n ( x ) = 1 for the Chebyshev polynomials of the first ( T n ) and second kind ( U n ). The results are established using necessary conditions of statistical optimal design theory for weighted polynomial regression. As special cases new identities are given for the Legendre, Chebyshev, ultraspherical, and Jacobi polynomials.
Kishor D Kucche - One of the best experts on this subject based on the ideXlab platform.
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On fractional Volterra integrodifferential equations with fractional integrable impulses
Mathematical Modelling and Analysis, 2019Co-Authors: Sagar T. Sutar, Kishor D KuccheAbstract:We consider a class of nonlinear fractional Volterra integrodifferential equation with fractional integrable impulses and investigate the existence and uniqueness results in the Bielecki’s normed Banach spaces. Further, Bielecki-Ulam type stabilities have been demonstrated on a Compact Interval. A concrete example is provided to illustrate the outcomes we acquired.
Miroslav Andrle - One of the best experts on this subject based on the ideXlab platform.
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Cardinal B-spline dictionaries on a Compact Interval
Applied and Computational Harmonic Analysis, 2005Co-Authors: Miroslav Andrle, Laura Rebollo-neiraAbstract:Abstract A prescription for constructing dictionaries for cardinal spline spaces on a Compact Interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a Compact Interval can be spanned by dictionaries of cardinal B-spline functions of broader support than the corresponding basis functions.