10,336 research outputs found

    A Fast Algorithm for the Inversion of Quasiseparable Vandermonde-like Matrices

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    The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and well-free Vandermonde-like matrices having O(n2)\mathcal{O}(n^2) complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2-term and 3-term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and well-free polynomials. Finally we present an O(n2)\mathcal{O}(n^2) algorithm to compute the inversion of quasiseparable Vandermonde-like matrices

    Signal Flow Graph Approach to Efficient DST I-IV Algorithms

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    In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST I-IV. The presented algorithms have low arithmetic cost compared to the known fast DST algorithms. Furthermore, the language of signal flow graph representation of digital structures is used to describe these efficient and recursive DST algorithms having (n�1) points signal flow graph for DST-I and n points signal flow graphs for DST II-IV

    Binding properties of the cell wall of Saccharomyces cerevisiae.

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    Reduced Multiplicative Complexity Discrete Cosine Transform (DCT) Circuitry

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    System and techniques for reduced multiplicative complex­ity discrete cosine transform (DCT) circuitry are described herein. An input data set can be received and, upon the input data set, a self-recursive DCT technique can be performed to produce a transformed data set. Here, the self-recursive DCT technique is based on a product of factors of a specified type of DCT technique. Recursive components of the technique are of the same DCT type as that of the DCT technique. The transformed data set can then be produced to a data con­sumer
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