This paper presents a parallel algorithm for finding the smallest eigenvalueof a particular form of ill-conditioned Hankel matrix, which requires the useof extremely high precision arithmetic. Surprisingly, we find thatcommonly-used approaches that are designed for high efficiency are actuallyless efficient than a direct approach under these conditions. We then develop aparallel implementation of the algorithm that takes into account the unusuallyhigh cost of individual arithmetic operations. Our approach combines messagepassing and shared memory, achieving near-perfect scalability and hightolerance for network latency. We are thus able to find solutions for muchlarger matrices than has been previously possible, with the potential forextending this work to systems with greater levels of parallelism.
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