Showing papers on "Biorthogonal system published in 1991"
Book•
27 Nov 1991
TL;DR: In this paper, the Christoffel-Darboux Identity and a Consequence was proven in a Vector Space using the Pade-type approximation of the Fredholm Equation.
Abstract: Introduction Preliminaries Biorthogonality and Applications Orthogonality for Polynomials Interpolation and Projection Kernel The Interpolation Operator The Method of Moments Lanczos' Method The Bi-conjugate Gradient Method Fredholm Equation and Pade-Type Approximants Adjacent Biorthogonal Families One-Step Forumlas Multistep Formulas Applications Sequence Transformations Linear Multistep Methods Approximation of Series Biorthogonal Polynomials Statistics and Least Squares Appendix 1: A Direct Proof of the Christoffel-Darboux Identity and a Consequence Appendix 2: Duality in Pade-Type Approximation Appendix 3: Sylvester's and Schweins' Identities in a Vector Space References
94 citations
TL;DR: In this paper, the authors obtained explicit bounds on the norms of biorthogonal functions to sets of complex exponentials where the { λ k } belong to a sector of the positive real axis.
44 citations
TL;DR: In this paper, the biorthogonal formulation of exchange perturbation theory does not run into difficulties when significant overlap occurs and numerical examples are presented to demonstrate that this is the case.
Abstract: Numerical examples are presented to demonstrate that the biorthogonal formulation of exchange perturbation theory, in contrast with common belief, does not run into difficulties when significant overlap occurs. Previously observed instabilities can be attributed to an improper partitioning of the hamiltonian, which, however, is commonly used in perturbation theories for intermolecular interactions.
17 citations
15 citations
14 citations
04 Nov 1991
TL;DR: Matrix descriptions of subband coders are introduced and used to obtain transform matrices of pyramidal and related algorithms and DFBs and pyramids optimal for quantization are also introduced.
Abstract: Matrix descriptions of subband coders are introduced and used to obtain transform matrices of pyramidal and related algorithms. These matrices are generalizations of the Haar matrix, and they are all shown to have a stratified structure related to circulant matrix structure. An implementation of a class of biorthogonal digital filter banks (DFBs) with an efficient predictive structure is introduced. DFBs and pyramids optimal for quantization are also introduced. >
5 citations
TL;DR: In this paper, the boundary-value problem of elasticity theory is considered for a rectangular semi-infinite strip whose long sides are free of stress, and separation of variables is used to reduce the solution to a series expansion of two functions defined in a closed interval (the “end” of the half-strip), in terms of homogeneous solutions.
4 citations
01 Jan 1991
TL;DR: The purpose of this work is to present and study new recursive filter banks with perfect reconstruction as an alternative to FIR (finite impulse response) filters which are commonly used in wavelet analysis.
Abstract: A new method is proposed for image coding involving two steps. First, the authors use a dual recursive wavelet transform in order to obtain a set of subclasses of images with better characteristics than the original image (lower entropy, edges discrimination, etc.). Secondly, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized. The purpose of this work is to present and study new recursive filter banks with perfect reconstruction as an alternative to FIR (finite impulse response) filters which are commonly used in wavelet analysis. The authors present two kinds of experimental results: coding of the well known Lena image with only two multiplications per pixel and then with an optimized IIR (infinite impulse response) filter.<>
2 citations
18 Nov 1991
TL;DR: A novel model of associative memory with biorthogonal properties is presented which can be viewed as an improved version of T. Kohonen's (1977) linear model of associations and can be more conveniently and unconditionally applied in any linear physical system.
Abstract: A novel model of associative memory with biorthogonal properties is presented which can be viewed as an improved version of T. Kohonen's (1977) linear model of associative memory. An iterative algorithm is developed which makes the proposed model directly usable without any limit condition. Several characteristics of the model which are very similar to biological phenomena are discussed. It is shown that the optimal value of an associative memory can always be obtained in the proposed model. Compared with Kohonen's model, the proposed model has many characteristics closer to the human functions of memory, and can be more conveniently and unconditionally applied in any linear physical system. >
2 citations
01 Jan 1991
TL;DR: Matrix descriptions of subband coders are introduced and used to obtain transform matrices of pyramidal and related algorithms and DFB's and pyramids optimal for quantization are also introduced.
Abstract: Matrix descriptions of subband coders are introduced and used to obtain transform matrices of pyramidal and related algorithms. These matrices are generalizations of the Haar matrix, and they are all shown to have a stratified structure related to circulant matrix structure. An implementation of a class of biorthogonal digital filter banks (DFB's) with an efficient predictive structure is introduced. DFB's and pyramids optimal for quantization are also introduced.
1 citations
TL;DR: In this article, a biorthogonal set is constructed for a basis of a band representation, and symmetry relations are established for the matrix connecting the BGS with the functions of the original basis.
Abstract: A biorthogonal set is constructed for a basis of a band representation. A simple fact is used that any band representation can be induced from a one‐dimensional representation of a point group (the latter is not necessarily an isotropy group of a Wyckoff position). It is shown that the biorthogonal set has the same symmetry structure as the original basis of the band representation. Symmetry relations are established for the matrix connecting the biorthogonal set with the functions of the original basis.