Browsing Department of Mathematics by Author "Li, Ren-Cang"
Now showing items 1-11 of 11
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A Bisection Method for the Banded Hyperbolic Quadratic Eigenvalue Problem
Ali, Ahmed T; 0000-0003-1436-8191 (2016-05-10)It is well-known that the eigenvalues of a Hermitian matrix in a given interval can be approximated within a predefined error tolerance using the bisection method as a direct application of the Sylvester's Law of Inertia. ... -
A Novel Regularized Orthonormalized Partial Least Squares Model for Multi-view Learning
Bian, Ce (2023-08-15)Over the past few years, the size of data dimensions or features has been increasing in various fields of science and engineering, owing to the rapid pace of data collection and the development of more advanced storage ... -
A NOVEL SUPERVISED DIMENSIONALITY REDUCTION METHOD: INTEGRATING PCA WITH SVM
Soleimani, Faezeh (2021-07-06)Data curation and storage methods have changed over the past few decades with the use of new technologies, and gathering data on a huge number of features (dimensions) is now very common among diverse scientific and ... -
NORMALIZED CUT PROBLEMS WITH GENERALIZED LINEAR CONSTRAINTS
Ruiz, Ivan; 0000-0003-3248-6271 (2019-08-30)Several methods are used to process images in many fields, including clustering, image segmentation and medical imaging. The so-called graph-cut methods in graph theory are widely used for image segmentation. In these ... -
Numerical Integration Of Matrix Riccati Differential Equations With Solution Singularities
Garrett, Charles K. (Mathematics, 2013-07-22)A matrix Riccati differential equation (MRDE) is a quadratic ODE of the form X' = A₂₁ + A₂₂X - XA₁₁ - XA₁₂X ; where X is a function of t with X : R Rnxm and the Aij's are constant or functions of t with matrix sizes ... -
NUMERICAL SOLUTION OF SADDLE POINT PROBLEMS BY PROJECTION
Karaduman, Gul (2017-12-04)In this thesis, we work on iterative solutions of large linear systems of saddle point problems of the form A B1 T B2 0 x y = f 0 , where A ∈ R n×n , B1, B2 ... -
Numerical Studies For M-Matrix Algebraic Riccati Equations
Wang, Weichao (Mathematics, 2013-10-22)A new doubling algorithm - Alternating-Directional Doubling Algorithm (ADDA) - is developed for computing the unique minimal nonnegative solution of an M-Matrix Algebraic Riccati Equation (MARE). It is argued by both ... -
On Optimizing the Sum of Rayleigh Quotients on the Unit Sphere
Binbuhaer, Aohud Abdulrahman (2019-05-06)Given symmetric matrices and positive definite matrices, we are concerned with the solution of the maximization of the function that is mentioned in the dissertation. We establish necessary optimality conditions for local ... -
Optimizing Krylov Subspace Methods for Linear Systems and Least Squares Problems
Yang, Mei (2018-08-10)The linear system and the linear least squares problem are two fundamental numerical linear algebra problems. Krylov subspace methods are the most practical and common techniques to build solvers. In this thesis, we focus ... -
OPTIMIZING L1 LOSS REGULARIZER AND ITS APPLICATION TO EEG INVERSE PROBLEM
Mainali, Kiran Kumar; 0000-0002-8510-8234 (2020-07-21)Sparse reconstruction occurs frequently in science and engineering and real-world applications, including statistics, finance, imaging, biological system, compressed sensing, and, today more than ever, machine learning and ... -
THREE DIMENSIONAL IMAGE RECONSTRUCTION (3DIRECT) OF SPARSE SIGNALS WITH MRI APPLICATION
Au, Melinda M; 0000-0001-8687-2640 (2016-11-29)Sparse signal reconstruction has been steadily gaining tremendous attention, specifically in applications of compressed sensing as well as feature selection in signal processing methods [IEEE Signal Processing, Vol. 25 ...