In this paper we introduce an algorithm for the construction of compactly supported interpolating scaling vectors on Rd with certain symmetry properties. In addition, we give an explicit construction method for corresponding symmetric dual scaling vectors and multiwavelets. As the main ingredients of our recipe we derive some implementable conditions for accuracy, symmetry, and biorthogonality ...

In 1996, we constructed periodic interpolatory scaling functions φj , wavelet functions Lj and their dual basis φ̃j and L̃j with properties such as symmetry, biorthogonality, any order of smoothness, real-valuedness, explicit expressions and interpolatory. We proved the localization of φj in 1997, and in 1998 with Li proved the localization of Lj . In this paper we shall give a detailed proof of ...

We introduce families of rational functions that are biorthogonal with respect to the $q$-hypergeometric distribution. A triplet $q$-difference operators $X$, $Y$, $Z$ is shown play a role analogous pair bispectral orthogonal polynomials. The recurrence relation and difference equation take form generalized eigenvalue problems involving three operators. algebra generated by akin algebras Askey-...

The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test pr...

Abstract In this article, we introduce the notion of nonuniform biorthogonal wavelets on positive half line. We first establish characterizations for translates a single function to form Riesz bases their closed linear span. provide complete characterization biorthogonality scaling functions two multiresolution analysis and associated wavelet families in $$L^2({\mathbb {R}}^+)$$ <mml:math xmlns...

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of orthogonal nonseparable bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is proposed by virtue of analogy method and iteration method. Their biorthogonality traits are researched by using time-frequency analysis approach and variable sepa...

We present the lifting scheme, a new idea for constructing compactly supported wavelets with compactly supported duals. The lifting scheme uses a simple relationship between all multiresolution analyses with the same scaling function. It isolates the degrees of freedom remaining after fixing the biorthogonality relations. Then one has full control over these degrees of freedom to custom design ...

This paper presents an error analysis of the Lanczos algorithm in finite-precision arithmetic for solving the standard nonsymmetric eigenvalue problem, if no breakdown occurs. An analog of Paige's theory on the relationship between the loss of orthogonality among the Lanczos vectors and the convergence of Ritz values in the symmetric Lanczos algorithm is discussed. The theory developed illustra...