Essays in Problems in Sequential Decisions and Large-Scale Randomized Algorithms

In the first part of this dissertation, we consider two problems in sequential decision making. The first problem we consider is sequential selection of a monotone subsequence from a random permutation. We find a two term asymptotic expansion for the optimal expected value of a sequentially selected monotone subsequence from a random permutation of length $n$. The second problem we consider deals with the multiplicative relaxation or constriction of the classical problem of the number of records in a sequence of $n$ independent and identically distributed observations. In the relaxed case, we find a central limit theorem (CLT) with a different normalization than Renyi\u27s classical CLT, and in the constricted case we find convergence in distribution to an unbounded random variable. In the second part of this dissertation, we put forward two large-scale randomized algorithms. We propose a two-step sensing scheme for the low-rank matrix recovery problem which requires far less storage space and has much lower computational complexity than other state-of-art methods based on nuclear norm minimization. We introduce a fast iterative reweighted least squares algorithm, \textit{Guluru}, based on subsampled randomized Hadamard transform, to solve a wide class of generalized linear models

Performance of Computer Systems; Proceedings of the 4th International Symposium on Modelling and Performance Evaluation of Computer Systems, Vienna, Austria, February 6-8, 1979

These proceedings are a collection of contributions to computer system performance, selected by the usual refereeing process from papers submitted to the symposium, as well as a few invited papers representing significant novel contributions made during the last year. They represent the thrust and vitality of the subject as well as its capacity to identify important basic problems and major application areas. The main methodological problems appear in the underlying queueing theoretic aspects, in the deterministic analysis of waiting time phenomena, in workload characterization and representation, in the algorithmic aspects of model processing, and in the analysis of measurement data. Major areas for applications are computer architectures, data bases, computer networks, and capacity planning. The international importance of the area of computer system performance was well reflected at the symposium by participants from 19 countries. The mixture of participants was also evident in the institutions which they represented: 35% from universities, 25% from governmental research organizations, but also 30% from industry and 10% from non-research government bodies. This proves that the area is reaching a stage of maturity where it can contribute directly to progress in practical problems