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31.
On vector subdivision 总被引:8,自引:0,他引:8
In this paper we give a complete characterization of the convergence of stationary vector subdivision schemes and the regularity
of the associated limit function. These results extend and complete our earlier work on vector subdivision and its use in
the construction of multiwavelets.
Received March 19, 1997; in final form November 13, 1997 相似文献
32.
Zhongying Chen Charles A. Micchelli Yuesheng Xu 《Advances in Computational Mathematics》2002,16(1):1-28
In this paper, we develop a discrete wavelet Petrov–Galerkin method for integral equations of the second kind with weakly singular kernels suitable for solving boundary integral equations. A compression strategy for the design of a fast algorithm is suggested. Estimates for the rate of convergence and computational complexity of the method are provided. 相似文献
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36.
Jianqiang Liu Charles A. Micchelli Rui Wang Yuesheng Xu 《Advances in Computational Mathematics》2013,38(2):427-439
Motivated by the importance of kernel-based methods for multi-task learning, we provide here a complete characterization of multi-task finite rank kernels in terms of the positivity of what we call its associated characteristic operator. Consequently, we are led to establishing that every continuous multi-task kernel, defined on a cube in an Euclidean space, not only can be uniformly approximated by multi-task polynomial kernels, but also can be extended as a multi-task kernel to all of the Euclidean space. Finally, we discuss the interpolation of multi-task kernels by multi-task finite rank kernels. 相似文献
37.
A determinantal identity, frequently used in the study of totally positive matrices, is extended, and then used to re-prove the well-known univariate knot insertion formula for B-splines. Also we introduce a class of matrices, intermediate between totally positive and strictly totally positive matrices. The determinantal identity is used to show any minor of such matrices is positive if and only if its diagonal entries are positive. Among others, this class of matrices includes B-splines collocation matrices and Hurwitz matrices.This author acknowledges a sabbatical stay at IBM T.J. Watson Research Center in 1990, which was supported by a DGICYT grant from Spain. 相似文献
38.
Charles A. Micchelli Lixin Shen Yuesheng Xu Xueying Zeng 《Advances in Computational Mathematics》2013,38(2):401-426
This paper introduces a proximity operator framework for studying the L1/TV image denoising model which minimizes the sum of a data fidelity term measured in the ?1-norm and the total-variation regularization term. Both terms in the model are non-differentiable. This causes algorithmic difficulties for its numerical treatment. To overcome the difficulties, we formulate the total-variation as a composition of a convex function (the ?1-norm or the ?2-norm) and the first order difference operator, and then express the solution of the model in terms of the proximity operator of the composition. By developing a “chain rule” for the proximity operator of the composition, we identify the solution as fixed point of a nonlinear mapping expressed in terms of the proximity operator of the ?1-norm or the ?2-norm, each of which is explicitly given. This formulation naturally leads to fixed-point algorithms for the numerical treatment of the model. We propose an alternative model by replacing the non-differentiable convex function in the formulation of the total variation with its differentiable Moreau envelope and develop corresponding fixed-point algorithms for solving the new model. When partial information of the underlying image is available, we modify the model by adding an indicator function to the minimization functional and derive its corresponding fixed-point algorithms. Numerical experiments are conducted to test the approximation accuracy and computational efficiency of the proposed algorithms. Also, we provide a comparison of our approach to two state-of-the-art algorithms available in the literature. Numerical results confirm that our algorithms perform favorably, in terms of PSNR-values and CPU-time, in comparison to the two algorithms. 相似文献
39.
Given two function spacesV 0,V 1 with compactly supported basis functionsC i, Fi, i∈Z, respectively, such thatC i can be written as a finite linear combination of theF i's, we study the problem of decomposingV 1 into a direct sum ofV 0 and some subspaceW ofV 1 in such a way thatW is spanned by compactly supported functions and that eachF i can be written as a finite linear combination of the basis functions inV 0 andW. The problem of finding such locally finite decompositions is shown to be equivalent to solving certain matrix equations involving two-slanted matrices. These relations may be reinterpreted in terms of banded matrices possessing banded inverses. Our approach to solving the matrix equations is based on factorization techniques which work under certain conditions on minors. In particular, we apply these results to univariate splines with arbitrary knot sequences. 相似文献
40.
Spectral factorization of Laurent polynomials 总被引:2,自引:0,他引:2
Goodman Tim N.T. Micchelli Charles A. Rodriguez Giuseppe Seatzu Sebastiano 《Advances in Computational Mathematics》1997,7(4):429-454
We analyse the performance of five numerical methods for factoring a Laurent polynomial, which is positive on the unit circle,
as the modulus squared of a real algebraic polynomial. It is found that there is a wide disparity between the methods, and
all but one of the methods are significantly influenced by the variation in magnitude of the coefficients of the Laurent polynomial,
by the closeness of the zeros of this polynomial to the unit circle, and by the spacing of these zeros.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献