We use singular value decomposition to approximate large, unmanage0 able matrices into
smaller invertible square matrices. Topics include the mathematics behind the singular …

In this dissertation, we discuss two distinct topics, both of which leverage randomized
algorithms in numerical linear algebra. First we study three variants of the Kaczmarz method …

Any m× n matrix can be factored into the product of an orthogonal matrix times a diagonal
matrix times another orthogonal matrix. This is called the Singular Value Decomposition …

We propose a new method for image reconstruction based on circulant matrices. The
novelty of this method is the image treatment using a simple and classical algebraic …

We propose a separable decomposition approximating the Karhunen-Loeve transform for
random fields. We show that this problem is related to a joint singular value decomposition …

In recent years, gradient-domain methods have been widely discussed in the image
processing field, including seamless cloning and image stitching. These algorithms are …

In many image processing applications, the discrete values of an image can be embedded
in a continuous function. This type of representation can be useful for interpolation …

Matrix algorithms based on orthogonal transformations play an important role in matrix
computations. Some of the reasons for this are:(1) Orthogonal transformations are …

Two aspects of the Kronecker product are studied. First, we start with the Kronecker product
approximation problem. Given a matrix A and a factorization of its dimensions, we find …

In this paper we propose an approach to approximate a truncated singular value
decomposition of a large structured matrix. By first decomposing the matrix into a sum of …