Necessary and sufficient conditions are given for the convergence of infinite products of matrices of complex numbers. The results are applied to the solution of periodic matrix refinement equations. Conditions are given for the solutions to be in L([0, 2π)) and generate a multiresolution of multiplicity r. A general algorithm for constructing multidimensional periodic multiwavelets from a scal...

We demonstrate the advantages of using multi-reolution analysis with multiwavelet basis with the Discontinuous Galerkin (DG) method. This provides significant enhancements to the standard DG methods. To illustrate the important gains of using the Multiwavelet DG method we apply it to conservation and convection diffusion problems in multiple dimensions. The significant benefits of merging DG me...

Multiwavelets are briefly reviewed and preprocessing and postprocessing for such wavelets are introduced. Least squares curve fitting of irregularly sampled data is achieved by means of unshifted and shifted multiscaling functions. This preprocessing procedure combined with multiwavelet neural networks for data-adaptive curve fitting is shown to perform well in the case of high resolution. In t...

Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signalprocessing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion, omnidirectional balancing, is introduc...

In applications using multiwavelets there is a necessary step of associating a given discrete signal with a function in the scaling function space V 0. This association is equivalent to including a preelter and a posttl-ter for the lterbank determined by the underlying multiwavelets. We give a construction for FIR orthogonal (paraunitary) preelters that preserve the approximation order of a giv...

In this paper multiwavelets based on two scaling functions are discussed. They exhibit the following properties: compact support, symmetry and orthogonality as well as a good frequency resolution. Lattice structures do not only o er the possibility to implement these multiwavelet transforms, the lattice rotation angles also can be used in order to parameterize all multiwavelets of a certain len...

Multiwavelets, wavelets with several scaling functions, offer simultaneous orthogonality, symmetry, and short support, which is not possible with ordinary (scalar) wavelets. These properties make multiwavelets promising for signal processing applications, such as image denoising. The common approach for image denoising is to get the multiwavelet decomposition of a noisy image and apply a common...

* This work is partially supported by NSC 99-2221-E-260-010-. † Correspondence to: D.-R. Duh; E-mail address: [email protected] Abstract – Floating-point matrix multiplier is widely used in scientific computations. A great deal of efforts has been made to achieve higher performance. The matrix multiplication consists of many multiplications and accumulations. Yang and Duh proposed a modular des...

Abstract In recent years the concept of multiresolution-based adaptive discontinuous Galerkin (DG) schemes for hyperbolic conservation laws has been developed. The key idea is to perform a multiresolution analysis DG solution using multiwavelets defined on hierarchy nested grids. Typically this applied dyadic grid hierarchies where explicit construction be performed only one reference element. ...