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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 ...
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 ...
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 analyze and implement the kernel ridge regression (KR) method developed in Filipovic et al. (Stripping the discount curve-a robust machine learning approach. Swiss Finance Institute Research Paper No. 22-24. SSRN. https://ssrn.com/abstract=4058150, 2022 ...
We introduce the class of linear-rational term structure models in which the state price density is modeled such that bond prices become linear-rational functions of the factors. This class is highly tractable with several distinct advantages: (i) ensures ...
This thesis studies the valuation and hedging of financial derivatives, which is fundamental for trading and risk-management operations in financial institutions. The three chapters in this thesis deal with derivatives whose payoffs are linked to interest ...
We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is eas ...
Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is their poor scalabili ...
This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...
