Making Matrices Better: Geometry and Topology of Singular Value and Polar Decomposition
نویسندگان
چکیده
منابع مشابه
Orthogonal Matrices and the Singular Value Decomposition
The first Section below extends to m × n matrices the results on orthogonality and projection we have previously seen for vectors. The Sections thereafter use these concepts to introduce the Singular Value Decomposition (SVD) of a matrix, the pseudo-inverse, and its use for the solution of linear systems.
متن کاملSingular value decomposition of multi-companion matrices
We obtain the singular value decomposition of multi-companion matrices. We completely characterise the columns of the matrix U and give a simple formula for obtaining the columns of the other unitary matrix, V , from the columns of U . We also obtain necessary and sufficient conditions for the related matrix polynomial to be hyperbolic.
متن کاملSingular Value Decomposition for Multidimensional Matrices
Singular Value Decomposition (SVD) is of great significance in theory development of mathematics and statistics. In this paper we propose the SVD for 3-dimensional (3-D) matrices and extend it to the general Multidimensional Matrices (MM). We use the basic operations associated with MM introduced by Solo to define some additional aspects of MM. We achieve SVD for 3-D matrix through these MM ope...
متن کاملParallel Singular Value Decomposition via the Polar Decomposition
A new method is described for computing the singular value decomposition (SVD). It begins by computing the polar decomposition and then computes the spectral decomposition of the Hermitian polar factor. The method is particularly attractive for shared memory parallel computers with a relatively small number of processors, because the polar decomposition can be computed efficiently on such machi...
متن کاملپیشنهاد 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...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2017
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti1571