In this dissertation, a fast numerical algorithm for computing the Markov renewal kernel via tight lower and upper bounds is developed. The Markov renewal kernel can then used to solve the well-known Markov renewal equation. Error analysis shows the numerically obtained bounds to be tight. The algorithm design and approximate solution process yield to a fast parallel solution methodology, which has speed-up behavior that is a linear function of the number of processors used. In particular, the parallel algorithm is of order O(k/2), when k is the number of processors used.
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机译：本文提出了一种通过紧上下限计算马尔可夫更新核的快速数值算法。然后，可以使用马尔可夫更新内核来求解众所周知的马尔可夫更新方程。误差分析表明，数值获得的边界是紧密的。算法设计和近似求解过程产生了一种快速并行求解方法，该方法具有加速行为，该行为是所使用处理器数量的线性函数。特别地，当 k 是所使用的处理器数量时，并行算法的顺序为 O （ k / 2）。
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