The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform

B J Falkowski - One of the best experts on this subject based on the ideXlab platform.

  • two classes of fixed polarity linearly independent arithmetic Transforms for quaternary functions
    European Signal Processing Conference, 2009
    Co-Authors: C C Lozano, B J Falkowski, Tadeusz Luba
    Abstract:

    Two classes of fixed polarity linearly independent arithmetic Transforms (FPQLIA) for quaternary functions are introduced in this paper. These Transforms are Kronecker-based and therefore can be calculated efficiently by Fast Transforms. Their basic definitions and Fast flow graphs are shown. Relations between the different FPQLIA Transforms are also presented and an algorithm for the optimization of FPQLIA is described which utilizes the given relation to reduce the computational cost. Experimental results for the Transforms in terms of the number of nonzero spectral coefficients in the optimal FPQLIA Transforms have also been given for several quaternary test functions and compared to the corresponding numbers for the optimal fixed polarity quaternary arithmetic (FPQA) Transforms. The results show that for the set of quaternary test functions the numbers for FPQLIA Transforms are on average 32% smaller than the ones for the FPQA Transforms.

  • ternary fixed polarity linear kronecker Transforms and their comparison with ternary reed muller transform
    Journal of Circuits Systems and Computers, 2005
    Co-Authors: B J Falkowski
    Abstract:

    Two new fixed polarity linear Kronecker Transforms executed over GF(3) are introduced in this article. Both Transforms are based on recursive equations using Kronecker products what allows to obtain simple corresponding Fast Transforms and very regular butterfly diagrams. The computational costs to calculate the new pair of Transforms and their experimental comparison with ternary Reed–Muller transform have also been discussed for the purpose of using their error correcting properties that are useful in circuit testing and verification.

  • kronecker based fixed polarity Transforms over gf 3
    Asia Pacific Conference on Circuits and Systems, 2004
    Co-Authors: B J Falkowski
    Abstract:

    Two new fixed polarity linear Kronecker Transforms executed over GF(3) are introduced in this article. Both Transforms are based on recursive equations using Kronecker products what allows to obtain simple corresponding Fast Transforms and very regular butterfly diagrams. The computational costs to calculate the new pair of Transforms and their experimental comparison with ternary Reed-Muller transform have also been discussed for the purpose of using their error correcting properties that are useful in circuit testing and verification.

  • Family of Fast linearly independent ternary arithmetic Transforms
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2004
    Co-Authors: B J Falkowski, Cheng Fu
    Abstract:

    In this paper, the family of Fast linearly independent ternary arithmetic (LITA) Transforms, which possesses Fast forward and inverse butterfly diagrams, has been identified. This family is recursively defined and has consistent formulas relating forward and inverse transform matrices. The LITA Transforms, which require horizontal or vertical permutations to have Fast Transforms are also discussed. Computational costs of the calculation for presented Transforms are also discussed and compared with multipolarity ternary arithmetic transform for ternary benchmark functions.

  • family of Fast Transforms over gf 3 logic
    International Symposium on Multiple-Valued Logic, 2003
    Co-Authors: B J Falkowski
    Abstract:

    New classes of recursive Transforms over GF(3) have been introduced here. They are based on simple recursive equations what allows to obtain corresponding Fast forward and inverse Transforms and very regular butterfly diagrams. The classification is further extended into various Transforms with horizontal and vertical permutations. The relations between various classes of introduced ternary Transforms are also discussed.

Martin Vetterli - One of the best experts on this subject based on the ideXlab platform.

  • ICASSP - Cyclic convolution of real sequences: Hartley versus Fourier and new schemes
    ICASSP '86. IEEE International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: Pierre Duhamel, Martin Vetterli
    Abstract:

    Recently, new Fast Transforms (such as the discrete Hartley transform in particular) have been proposed which are best suited for the computation of cyclic convolution of real sequences. Two approaches using Fourier or Hartley Transforms are first compared, showing that the recently proposed FFT algorithms for real data present a lower arithmetic complexity than the corresponding DHT-based approach. Improvements are made to both types of algorithms, leading to different trade offs between arithmetic and structural complexity. We also present a new Hartley Transform algorithm with lower arithmetic complexity than any previously published one.

Kurt Otto - One of the best experts on this subject based on the ideXlab platform.

  • on software support for finite difference schemes based on index notation
    International Conference on Computational Science, 2002
    Co-Authors: Krister Åhlander, Kurt Otto
    Abstract:

    A formulation of finite difference schemes based on the index notation of tensor algebra is advocated. Finite difference operators on regular grids may be described as sparse, banded, "tensors". Especially for 3D, it is claimed that index notation better corresponds to the inherent problem structure than does conventional matrix notation. The transition from mathematical index notation to implementation is discussed. Software support for index notation that obeys the Einstein summation convention has been implemented in the C++ package Ein-Sum. The extension of EinSum to support typical data structures of finite difference schemes is outlined. A combination of general index notation software and special-purpose routines for instance for Fast Transforms is envisioned.

  • International Conference on Computational Science (3) - On Software Support for Finite Difference Schemes Based on Index Notation
    Lecture Notes in Computer Science, 2002
    Co-Authors: Krister Åhlander, Kurt Otto
    Abstract:

    A formulation of finite difference schemes based on the index notation of tensor algebra is advocated. Finite difference operators on regular grids may be described as sparse, banded, "tensors". Especially for 3D, it is claimed that index notation better corresponds to the inherent problem structure than does conventional matrix notation. The transition from mathematical index notation to implementation is discussed. Software support for index notation that obeys the Einstein summation convention has been implemented in the C++ package Ein-Sum. The extension of EinSum to support typical data structures of finite difference schemes is outlined. A combination of general index notation software and special-purpose routines for instance for Fast Transforms is envisioned.

  • iterative solution of the helmholtz equation by a second order method
    SIAM Journal on Matrix Analysis and Applications, 1999
    Co-Authors: Kurt Otto, Elisabeth Larsson
    Abstract:

    The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions is studied. The specific problem is the propagation of hydroacoustic waves in a two-dimensional curvilinear duct. The problem is discretized with a second-order accurate finite difference method, resulting in a linear system of equations. To solve the system of equations, a preconditioned Krylov subspace method is employed. We construct a preconditioner that is based on Fast Transforms and yields a direct Fast Helmholtz solver for rectangular domains. Numerical experiments for curved ducts demonstrate that the rate of convergence is high. The Fast transform preconditioner is compared with a symmetric successive over-relaxation (SSOR) preconditioner, and also with band Gaussian elimination. For the preconditioned iterative methods, the gains in storage requirement are large compared with band Gaussian elimination. Regarding the arithmetic complexity, the Fast transform preconditioner yields a significant gain, whereas the SSOR preconditioner performs worse than band Gaussian elimination.

  • A framework for polynomial preconditioners based on Fast Transforms I: Theory
    BIT Numerical Mathematics, 1998
    Co-Authors: Sverker Holmgren, Kurt Otto
    Abstract:

    Optimal and superoptimal approximations of a complex square matrix by polynomials in a normal basis matrix are considered. If the unitary transform associated with the eigenvectors of the basis matrix is computable using a Fast algorithm, the approximations may be utilized for constructing preconditioners. Theorems describing how the parameters of the approximations could be efficiently computed are given, and for special cases earlier results by other authors are recovered. Also, optimal and superoptimal approximations for block matrices are determined, and the same type of theorems as for the point case are proved.

  • A framework for polynomial preconditioners based on Fast Transforms II: PDE applications
    BIT Numerical Mathematics, 1998
    Co-Authors: Sverker Holmgren, Kurt Otto
    Abstract:

    The solution of systems of equations arising from systems of time-dependent partial differential equations (PDEs) is considered. Primarily, first-order PDEs are studied, but second-order derivatives are also accounted for. The discretization is performed using a general finite difference stencil in space and an implicit method in time. The systems of equations are solved by a preconditioned Krylov subspace method. The preconditioners exploit optimal and superoptimal approximations by low-degree polynomials in a normal basis matrix, associated with a Fast trigonometric transform. Numerical experiments for high-order accurate discretizations are presented. The results show that preconditioners based on Fast Transforms yield efficient solution algorithms, even for large quotients between the time and space steps. Utilizing a spatial grid ratio less than one, the arithmetic work per grid point is bounded by a constant as the number of grid points increases.

Pierre Duhamel - One of the best experts on this subject based on the ideXlab platform.

  • ICASSP - Cyclic convolution of real sequences: Hartley versus Fourier and new schemes
    ICASSP '86. IEEE International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: Pierre Duhamel, Martin Vetterli
    Abstract:

    Recently, new Fast Transforms (such as the discrete Hartley transform in particular) have been proposed which are best suited for the computation of cyclic convolution of real sequences. Two approaches using Fourier or Hartley Transforms are first compared, showing that the recently proposed FFT algorithms for real data present a lower arithmetic complexity than the corresponding DHT-based approach. Improvements are made to both types of algorithms, leading to different trade offs between arithmetic and structural complexity. We also present a new Hartley Transform algorithm with lower arithmetic complexity than any previously published one.

Bogdan J. Falkowski - One of the best experts on this subject based on the ideXlab platform.

  • TERNARY RECURSIVE Fast Transforms: PROPERTIES, MUTUAL RELATIONS, AND CIRCUIT REALIZATION
    Journal of Circuits Systems and Computers, 2007
    Co-Authors: Bogdan J. Falkowski
    Abstract:

    This paper introduces two new classes of recursive Fast Transforms over GF (3). They are based on recursive equations using Kronecker products that allows to obtain simple corresponding Fast transf...

  • TERNARY RECURSIVE Fast Transforms
    Journal of Circuits Systems and Computers, 2007
    Co-Authors: Bogdan J. Falkowski
    Abstract:

    This paper introduces two new classes of recursive Fast Transforms over GF (3). They are based on recursive equations using Kronecker products that allows to obtain simple corresponding Fast Transforms and regular butterfly diagrams. The computational costs to calculate both classes of new Transforms and the experimental results comparing introduced Transforms with ternary Reed–Muller transform are also presented.

  • Two classes of recursive Fast Transforms over GF(3): properties, relations and computational costs
    The 2004 IEEE Asia-Pacific Conference on Circuits and Systems 2004. Proceedings., 1
    Co-Authors: Bogdan J. Falkowski
    Abstract:

    This work introduces two new classes of recursive Fast Transforms over GF(3). They are based on recursive equations using Kronecker products what allows to obtain simple corresponding Fast Transforms and regular butterfly diagrams. The computational costs to calculate both classes of new Transforms and the experimental results comparing introduced Transforms with ternary Reed-Muller transform are also presented.

  • ISMVL - Family of Fast Transforms over GF(3) logic
    33rd International Symposium on Multiple-Valued Logic 2003. Proceedings., 1
    Co-Authors: Bogdan J. Falkowski
    Abstract:

    New classes of recursive Transforms over GF(3) have been introduced here. They are based on simple recursive equations what allows to obtain corresponding Fast forward and inverse Transforms and very regular butterfly diagrams. The classification is further extended into various Transforms with horizontal and vertical permutations. The relations between various classes of introduced ternary Transforms are also discussed.