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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 59 (1991), S. 453-472 
    ISSN: 0945-3245
    Keywords: 65F05 ; 65G99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two methods are presented which efficiently solve tridiagonal systems on vector supercomputers and parallel computers with a moderate degree of parallelism. The first algorithm for diagonally dominant systems uses incomplete Gaussian elimination, the other for more general systems applies Gaussian elimination with partial pivoting. The methods are based on wrap-around partitioning, which is closely related to the partitioning used in Wang's algorithm. The first algorithm delivers an asymptotic speedup by a factor ofp on ap-processor computer if compared to the scalar algorithm, whereas the second algorithm delivers a speedup by a factor of roughlyp/2, which is also typical for cyclic reduction. For the incomplete factorization, existence and approximation properties are proved. Timing experiments were run on a Cray X-MP.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 68 (1994), S. 507-547 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65T20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We propose a new algorithm for fast Fourier transforms. This algorithm features uniformly long vector lengths and stride one data access. Thus it is well adapted to modern vector computers like the Fujitsu VP2200 having several floating point pipelines per CPU and very fast stride one data access. It also has favorable properties for distributed memory computers as all communication is gathered together in one step. The algorithm has been implemented on the Fujitsu VP2200 using the basic subroutines for fast Fourier transforms discussed elsewhere. We develop the theory of index digit permutations to some extent. With this theory we can derive the splitting formulas for almost all mixed-radix FFT algorithms known so far. This framework enables us to prove these algorithms but also to derive our new algorithm. The development and systematic use of this framework is new and allows us to simplify the proofs which are now reduced to the application of matrix recursions.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Computational statistics 15 (2000), S. 463-484 
    ISSN: 1613-9658
    Keywords: Keywords: MARS, B-splines, Data Mining, Parallel Algorithms.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We investigate one of the possible ways for improving Friedman's Multivariate Adaptive Regression Splines (MARS) algorithm designed for flexible modelling of high-dimensional data. In our version of MARS called BMARS we use B-splines instead of truncated power basis functions. The fact that B-splines have compact support allows us to introduce the notion of a “scale” of a basis function. The algorithm starts building up models by using large-scale basis functions and switches over to a smaller scale after the fitting ability of the large scale splines has been exhausted. The process is repeated until the prespecified number of basis functions has been produced. In addition, we discuss a parallelisation of BMARS as well as an application of the algorithm to processing of a large commercial data set. The results demonstrate the computational efficiency of our algorithm and its ability to generate models competitive with those of the original MARS.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 38 (1987), S. 785-790 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 42 (1991), S. 468-470 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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