Andrei Osipov Libros

Focusing on the computational challenges of finding nearest neighbors in high-dimensional spaces, the book introduces a randomized approximate algorithm that significantly reduces the operational costs compared to traditional methods. While the naive approach can be prohibitively time-consuming, especially with large datasets, this new algorithm offers a practical solution for applications in data mining, image processing, and machine learning. The text includes a probabilistic analysis and showcases the algorithm's effectiveness through numerical experiments.

Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs have been becoming a popular computational tool. The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematicians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.