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Asymptotically tight worst case complexity bounds for initial-value problems with nonadaptive information

机译:具有非自适应信息的初值问题的渐近严格最坏情况复杂度范围

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摘要

It is known that, for systems of initial-value problems, algorithms using adaptive information perform much better in the worst case setting than the algorithms using nonadaptive information. In the latter case, lower and upper complexity bounds significantly depend on the number of equations. However, in contrast with adaptive information, existing lower and upper complexity bounds for nonadaptive information are not asymptotically tight. In this paper, we close the gap in the complexity exponents, showing asymptotically matching bounds for nonadaptive standard information, as well as for a more general class of nonadaptive linear information. (C) 2018 Elsevier Inc. All rights reserved.
机译:众所周知,对于具有初值问题的系统,使用自适应信息的算法在最坏情况下的性能要比使用非自适应信息的算法好得多。在后一种情况下,复杂度的上限和下限在很大程度上取决于方程式的数量。但是,与自适应信息相反,非自适应信息的现有较低和较高复杂度边界不是渐近严格的。在本文中,我们缩小了复杂度指数的差距,显示了非自适应标准信息以及非常规线性信息的一类渐近匹配范围。 (C)2018 Elsevier Inc.保留所有权利。

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