Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
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TL;DR: A symmetric version of the nonsymmetric mixed finite element method for nearly incompressible elasticity that can statically condense out all auxiliary variables from the saddle point problem arriving at a symmetric and positive‐definite system based only on the displacement.
Abstract: We present a symmetric version of the nonsymmetric mixed finite element method presented in (Lamichhane, ANZIAM J 50 (2008), C324–C338) for nearly incompressible elasticity. The displacement–pressure formulation of linear elasticity is discretized using a Petrov–Galerkin discretization for the pressure equation in (Lamichhane, ANZIAM J 50 (2008), C324–C338) leading to a non-symmetric saddle point problem. A new three-field formulation is introduced to obtain a symmetric saddle point problem which allows us to use a biorthogonal system. Working with a biorthogonal system, we can statically condense out all auxiliary variables from the saddle point problem arriving at a symmetric and positive-definite system based only on the displacement. We also derive a residual based error estimator for the mixed formulation of the problem. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012
19 citations
TL;DR: A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed in this paper, where simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are found.
Abstract: A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are found. A connection of the kernel of this transform with biorthogonal rational functions is observed.
19 citations
01 Jun 1998
TL;DR: New algorithms for the computation of orthogonal and biorthogonal modulated lapped transforms (MLTs) are presented and it is demonstrated that the multiplicative complexity of the Orthogonal MLT is the same as that of the DCT-IV.
Abstract: New algorithms for the computation of orthogonal and biorthogonal modulated lapped transforms(MLTs) are presented. The new structures are obtained by combining the MLT window operators with stages from a previously introduced structure for the type-IV discrete cosine transform (DCT-IV). The net result is fewer multiplications and additions than previously reported algorithms. For the orthogonal MLT, in particular, the new structure requires the computation of a slightly modified DCT-IV and some extra additions, but no further multiplications; so it demonstrates that the multiplicative complexity of the orthogonal MLT is the same as that of the DCT-IV.
19 citations
TL;DR: In this paper, the authors studied the characterization of two-overlapping dual window functions that give rise to biorthogonal Schauder bases, frames, and Riesz bases by modulation of the cosines.
Abstract: This paper is devoted to the study of characterization of two-overlapping dual window functions that give rise to biorthogonal Schauder bases, frames, and Riesz bases by modulation of the cosines. We show that in this case any frame is a Riesz basis and our characterization of Riesz bases may be considered as a generalization of the theorems established by Coifman, et al. [6] and by Jawerth and Sweldens [9].
19 citations
TL;DR: It is shown that the construction of biorthogonal M- channel wavelet bases is equivalent to the design of a M-channel perfect reconstruction filter bank with some added regularity conditions.
Abstract: We generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M-channel. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal M-channel wavelet bases is equivalent to the design of a M-channel perfect reconstruction filter bank with some added regularity conditions. A family of M-channel biorthogonal wavelet bases based on the cosine-modulated filter bank (CMFB) is proposed. It has the advantages of simple design procedure, efficient implementation, and good filter quality. A new method fur imposing the regularity on the CMFBs is also introduced, and several design examples are given.
19 citations