| Summary: | 博士 === 國立高雄應用科技大學 === 機械工程系 === 105 === There are three main results in this paper. Firstly, we consider the problem of searching for a vector of multipliers in a full period two-term third-order multiple recursive generator (MRG) with the objective of maximizing the spectral test performance. An approximate spectral test by considering the basis reduction is proposed. Sixteen variants of the approximate spectral test are evaluated by ten performance measures and running time. The spectral value found by the backward heuristic with approximate spectral test is superior to the best previously published one for the full period third-order MRG. Secondly, we present an explicit upper bound on spectral test of dimensions less than and equal to 2k for a two-term kth-order MRG with same multipliers. According to an exhaustive search we perform, the results indicate differences of the upper bound on spectral test exist among the order, the dimension and the number of multipliers vectors. Finally, we conduct some computational experiments to exhaustive searches for the worst-case spectral test of DX and DL MRGs. The results indicate differences of the spectral test exist among the order, the generator and the number of multipliers vectors. We demonstrate that these differences can affect the worst-case performance of spectral tests.
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