We study the worst case tractability of multivariate linear problems defined on separable Hilbert spaces. Information about a problem instance consists of noisy evaluations of arbitrary bounded linear functionals, where the noise is either deterministic or random. The cost of a single evaluation depends on its precision and is controlled by a cost function. We establish mutual interactions between tractability of a problem with noisy information, the cost function, and tractability of the same problem, but with exact information.
翻译:我们研究了在可分离的Hilbert空间中定义的多元线性问题在最劣情况下在噪声信息存在下的可处理性。问题实例的信息包括任意有界线性泛函的噪声评估,其中噪声是确定性或随机的。单个评估的成本取决于其精度,并由成本函数控制。我们建立了在噪声信息和精确信息下,问题的可处理性和成本函数之间的相互作用。