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Full-Text Articles in Physical Sciences and Mathematics
Singular Value Computation And Subspace Clustering, Qiao Liang
Singular Value Computation And Subspace Clustering, Qiao Liang
Theses and Dissertations--Mathematics
In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, …
Analysis And Constructions Of Subspace Codes, Carolyn E. Troha
Analysis And Constructions Of Subspace Codes, Carolyn E. Troha
Theses and Dissertations--Mathematics
Random network coding is the most effcient way to send data across a network, but it is very susceptible to errors and erasures. In 2008, Kotter and Kschischang introduced subspace codes as an algebraic approach to error correcting in random network coding. Since this paper, there has been much work in constructing large subspace codes, as well as exploring the properties of such codes. This dissertation explores properties of one particular construction and introduces a new construction for subspace codes. We begin by exploring properties of irreducible cyclic orbit codes, which were introduced in 2011 by Rosenthal et al. As …
The Krylov Subspace Methods For The Computation Of Matrix Exponentials, Hao Wang
The Krylov Subspace Methods For The Computation Of Matrix Exponentials, Hao Wang
Theses and Dissertations--Mathematics
The problem of computing the matrix exponential etA arises in many theoretical and practical problems. Many methods have been developed to accurately and efficiently compute this matrix function or its product with a vector, i.e., etAv. In the past few decades, with the increasing need of the computation for large sparse matrices, iterative methods such as the Krylov subspace methods have proved to be a powerful class of methods in dealing with many linear algebra problems. The Krylov subspace methods have been introduced for computing matrix exponentials by Gallopoulos and Saad, and the corresponding error bounds …