Nonlinear ill-posed equations: Singular value decomposition and the Picard criterion

Generalizable Singular Value Decomposition for Ill-posed Datasets

Stephen C. Strother PET Imaging Service VA medical center Minneapolis steve@pet. med. va. gov We demonstrate that statistical analysis of ill-posed data sets is subject to a bias, which can be observed when projecting independent test set examples onto a basis defined by the training examples. Because the training examples in an ill-posed data set do not fully span the signal space the observed...

پیشنهاد روش جدیدی برای محاسبه polynomial singular value decomposition ) psvd )

در این پایان نامه به معرفی روشهای مختلف محاسبه psvd می پردازیم. بخشی از این روشها به بررسی روشهای مختلف محاسبه psvd در مقالات مطالعه شده می پردازد که می توان به محاسبهpsvd با استفاده از الگوریتمهای pqrd و pevd و sbr2 و محاسبه psvd براساس تکنیک kogbetliantz و روش پارامتریک برای محاسبه psvd اشاره نمود. بخش بعدی نیز به بررسی روشهای مستقیم پیشنهادی محاسبه psvd برای ماتریسهای 2×2و2× n و n×2 و 3× n و...

Regularization of Nonlinear Ill-posed Equations with Accretive Operators

We study the regularization methods for solving equations with arbitrary accretive operators. We establish the strong convergence of these methods and their stability with respect to perturbations of operators and constraint sets in Banach spaces. Our research is motivated by the fact that the fixed point problems with nonexpansive mappings are namely reduced to such equations. Other important ...

On Solvability of Ill Posed Initial–boundary Value Problems for Higher Order Nonlinear Hyperbolic Equations

Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD)

The singular value decomposition (SVD) is a generalization of the eigen-decomposition which can be used to analyze rectangular matrices (the eigen-decomposition is definedonly for squaredmatrices). By analogy with the eigen-decomposition, which decomposes a matrix into two simple matrices, the main idea of the SVD is to decompose a rectangular matrix into three simple matrices: Two orthogonal m...