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We establish essentially optimal bounds on the complexity of initial-value problems in the ran-domized and quantum settings. We define for this purpose a sequence of new algorithms, whose error/cost properties improve from step to step. This leads to new upper complexity bounds, which differ from known lower bounds only by an arbitrarily small positive… (More)

We study the problem, initiated in [8], of finding randomized and quantum complexity of initial-value problems. We showed in [8] that a speed-up in both settings over the worst-case deterministic complexity is possible. In the present paper we prove, by defining new algorithms, that further improvement in upper bounds on the randomized and quantum… (More)

Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers with respect to deterministic and randomized algorithms on a classical computer. In this paper we deal with the randomized… (More)

Restricted complexity estimation is a major topic in control-oriented identiica-tion. Conditional algorithms are used to identify linear nite dimensional models of complex systems, the aim being to minimize the worst-case identiication error. High computational complexity of optimal solutions suggests to employ suboptimal estimation algorithms. This paper… (More)