198 research outputs found

    D-optimal matrices of orders 118, 138, 150, 154 and 174

    Full text link
    We construct supplementary difference sets (SDS) with parameters (59;28,22;21)(59;28,22;21), (69;31,27;24)(69;31,27;24), (75;36,29;28)(75;36,29;28), (77;34,31;27)(77;34,31;27) and (87;38,36;31)(87;38,36;31). These SDSs give D-optimal designs (DO-designs) of two-circulant type of orders 118,138,150,154 and 174. Until now, no DO-designs of orders 138,154 and 174 were known. While a DO-design (not of two-circulant type) of order 150 was constructed previously by Holzmann and Kharaghani, no such design of two-circulant type was known. The smallest undecided order for DO-designs is now 198. We use a novel property of the compression map to speed up some computations.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1409.596

    Mersenne Primes, Polygonal Anomalies and String Theory Classification

    Get PDF
    It is pointed out that the Mersenne primes Mp=(2p1)M_p=(2^p-1) and associated perfect numbers Mp=2p1Mp{\cal M}_p=2^{p-1}M_p play a significant role in string theory; this observation may suggest a classification of consistent string theories.Comment: 10 pages LaTe

    How Fast Can We Multiply Large Integers on an Actual Computer?

    Full text link
    We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity of a task like multiplication of long integers. The Turing machine is more useful here, but fails to take into account the multiplication instruction for short integers, which is available on physical computing devices. An interesting outcome is that the proposed refined complexity measures do not rank the well known multiplication algorithms the same way as the Turing machine model.Comment: To appear in the proceedings of Latin 2014. Springer LNCS 839

    A GPU-based hyperbolic SVD algorithm

    Get PDF
    A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU--GPU parallelism are discussed.Comment: Accepted for publication in BIT Numerical Mathematic
    corecore