2 citations · 6 across the 7 of their papers we have counts for
7 papers
Efficient finite-dimensional solution of initial value problems in infinite-dimensional Banach spaces
Boleslaw Kacewicz, Pawel Przybylowicz
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 t…
Asymptotically tight worst case complexity bounds for initial-value problems with nonadaptive information
Boleslaw Kacewicz
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 i…
Adaptive mesh selection asymptotically guarantees a prescribed local error for systems of initial value problems
Boleslaw Kacewicz
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 opti…
Adaptive mesh point selection for the efficient solution of scalar IVPs
Boleslaw Kacewicz
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 l…
Almost Optimal Solution of Initial-Value Problems by Randomized and Quantum Algorithms
Boleslaw Kacewicz
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…
Improved Bounds on the Randomized and Quantum Complexity of Initial-Value Problems
Boleslaw Kacewicz
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…
Randomized and Quantum Algorithms Yield a Speed-Up for Initial-Value Problems
Boleslaw Kacewicz
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 pro…