In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...
In this thesis we present three closed form approximation methods for portfolio valuation and risk management.The first chapter is titled ``Kernel methods for portfolio valuation and risk management'', and is a joint work with Damir Filipovi'c (SFI and ...
Using data on international equity portfolio allocations by U.S. mutual funds, we estimate a portfolio expression derived from a standard mean-variance portfolio model extended with portfolio frictions. The optimal portfolio depends on the previous month a ...
We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...
This thesis uses machine learning techniques and text data to investigate the relationships that arise between the Fed and financial markets, and their consequences for asset prices.The first chapter, entitled Market Expectations and the Impact of Unconv ...
Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...
We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...
This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and
considerations of statistical and com ...
Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smal ...
