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 ...
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 ...
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 ...
With the advent of emerging technologies and the Internet of Things, the importance of online data analytics has become more pronounced. Businesses and companies are adopting approaches that provide responsive analytics to stay competitive in the global ma ...
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 ...
Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matri ...
FPGAs rely on massive datapath parallelism to accelerate applications even with a low clock frequency. However, applications such as sparse linear algebra and graph analytics have their throughput limited by irregular accesses to external memory for which ...
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 ...
We present a nonparametric 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 easy ...
In this thesis we address the computation of a spectral decomposition for symmetric
banded matrices. In light of dealing with large-scale matrices, where classical dense
linear algebra routines are not applicable, it is essential to design alternative tech ...
