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Absolute value information for IBC problems
Journal of Complexity ( IF 1.338 ) Pub Date : 2019-08-24 , DOI: 10.1016/j.jco.2019.101427
Leszek Plaskota; Paweł Siedlecki; Henryk Woźniakowski

Two classes of information have been mainly considered in Information-Based Complexity (IBC) for approximate solutions of continuous problems. The first class is Λall and consists of all linear functionals, whereas the second class is Λstd and consists of only function evaluations. A different class of information has been studied in the context of phase retrieval, where it is assumed that only absolute values of linear functionals from ΛΛall are available. We denote this class |Λ| and call it the absolute value information class. For |Λ| we need to modify the algorithm error to compensate the missing phase in information values.

The purpose of this paper is to establish the powers of |Λall| and |Λstd| in comparison to Λall and Λstd for various IBC problems in the worst case setting. Our main result is that |Λall| is roughly of the same power as Λall for linear IBC problems. On the other hand, |Λstd| is usually too weak to solve linear problems.

更新日期:2020-01-04

 

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