Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Kacewicz, Bolesław"'
We deal with the approximate solution of initial value problems in infinite-dimensional Banach spaces with a Schauder basis. We only allow finite-dimensional algorithms acting in the spaces $\rr^N$, with varying $N$. The error of such algorithms depe
Externí odkaz:
http://arxiv.org/abs/1712.06514
Autor:
Kacewicz, Boleslaw
Publikováno v:
J. Complexity, 47, 86-96, 2018
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 sign
Externí odkaz:
http://arxiv.org/abs/1709.09951
Autor:
Kacewicz, Boleslaw
Publikováno v:
Adv. Comput. Math. Vol. 44, 5, 1325-1344, 2018
We study adaptive mesh selection for the solution of systems of initial value problems. The goal is a rigorous theoretical analysis of potential advantages of adaption. For an optimal method in the sense of the speed of convergence, we propose an alg
Externí odkaz:
http://arxiv.org/abs/1704.01939
Autor:
Kacewicz, Boleslaw
Publikováno v:
Numerical Algorithms 77(1), 57-75, 2018
We discuss adaptive mesh point selection for the solution of scalar IVPs. We consider a method that is optimal in the sense of the speed of convergence, and aim at minimizing the local errors. Although the speed of convergence cannot be improved by u
Externí odkaz:
http://arxiv.org/abs/1612.02749
Publikováno v:
In Journal of Mathematical Analysis and Applications March 2019 471(1-2):322-341
Autor:
Kacewicz, Boleslaw
Publikováno v:
Journal of Complexity 22 (2006), 676-690
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These algorithm
Externí odkaz:
http://arxiv.org/abs/quant-ph/0510045
Autor:
Kacewicz, Boleslaw
Publikováno v:
Journal of Complexity 21 (2005), 740-756
We deal with 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 pr
Externí odkaz:
http://arxiv.org/abs/quant-ph/0405018
Autor:
Kacewicz, Boleslaw
Publikováno v:
Journal of Complexity 20 (2004) 821-834
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
Externí odkaz:
http://arxiv.org/abs/quant-ph/0311148