東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

On the Elementary Symmetric Polynomi...

Chen, Lixiang .

FindBook

Google Book

Amazon

博客來

On the Elementary Symmetric Polynomials, Inverse Vandermonde Matrix, and Its Application in Signals and Images.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	On the Elementary Symmetric Polynomials, Inverse Vandermonde Matrix, and Its Application in Signals and Images./
作者:	Chen, Lixiang .
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	111 p.
附註:	Source: Masters Abstracts International, Volume: 82-01.
Contained By:	Masters Abstracts International82-01.
標題:	Electrical engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27832781
ISBN:	9798662395640

On the Elementary Symmetric Polynomials, Inverse Vandermonde Matrix, and Its Application in Signals and Images.
Chen, Lixiang .

On the Elementary Symmetric Polynomials, Inverse Vandermonde Matrix, and Its Application in Signals and Images. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 111 p.

Source: Masters Abstracts International, Volume: 82-01.

Thesis (M.A.S.)--University of Toronto (Canada), 2020.

This item must not be sold to any third party vendors.

The Vandermonde matrix naturally appears in systems of equations for applications of polynomial approximation. Solving the system, which requires inverting the Vandermonde matrix, may be preferred because researchers can utilize efficient matrix computation methods. However, the Vandermonde is ill-conditioned and prevents standard methods from calculating accurate entries to the inverse. Many of the derived algorithmic solutions to the Vandermonde inverse contain a mathematical expression called the Elementary Symmetric Polynomial (ESP). The ESP is computationally inefficient to solve directly, so there are also algorithms to solve them. The state-of-the-art ESP and inverse methods are fully recursive and may be more susceptible to noise perturbations in the Vandermonde matrix than a closed-form inverse method. In addition, the performances of the methods in a variety of applications in polynomial approximation are unexplored. This thesis investigates the utility of the state-of-the-art methods against a novel ESP and closed-form Vandermonde inverse method in applications of polynomial interpolation and Fourier reconstruction in the presence of Gaussian noise.

ISBN: 9798662395640Subjects--Topical Terms:

649834
Electrical engineering.
Subjects--Index Terms:

Elementary symmetric polynomial

On the Elementary Symmetric Polynomials, Inverse Vandermonde Matrix, and Its Application in Signals and Images.
LDR:02350nmm a2200349 4500 001 2276676
005 20210510091847.5
008 220723s2020 ||||||||||||||||| ||eng d
020 $a 9798662395640
035 $a (MiAaPQ)AAI27832781
035 $a AAI27832781
040 $a MiAaPQ $c MiAaPQ
100 1 $a Chen, Lixiang . $3 3554968
245 1 0 $a On the Elementary Symmetric Polynomials, Inverse Vandermonde Matrix, and Its Application in Signals and Images.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 111 p.
500 $a Source: Masters Abstracts International, Volume: 82-01.
500 $a Advisor: Plataniotis, Konstantinos N.
502 $a Thesis (M.A.S.)--University of Toronto (Canada), 2020.
506 $a This item must not be sold to any third party vendors.
520 $a The Vandermonde matrix naturally appears in systems of equations for applications of polynomial approximation. Solving the system, which requires inverting the Vandermonde matrix, may be preferred because researchers can utilize efficient matrix computation methods. However, the Vandermonde is ill-conditioned and prevents standard methods from calculating accurate entries to the inverse. Many of the derived algorithmic solutions to the Vandermonde inverse contain a mathematical expression called the Elementary Symmetric Polynomial (ESP). The ESP is computationally inefficient to solve directly, so there are also algorithms to solve them. The state-of-the-art ESP and inverse methods are fully recursive and may be more susceptible to noise perturbations in the Vandermonde matrix than a closed-form inverse method. In addition, the performances of the methods in a variety of applications in polynomial approximation are unexplored. This thesis investigates the utility of the state-of-the-art methods against a novel ESP and closed-form Vandermonde inverse method in applications of polynomial interpolation and Fourier reconstruction in the presence of Gaussian noise.
590 $a School code: 0779.
650 4 $a Electrical engineering. $3 649834
650 4 $a Applied mathematics. $3 2122814
653 $a Elementary symmetric polynomial
653 $a Magnetic resonance imaging
653 $a Vandermonde inverse
653 $a Vandermonde matrix
690 $a 0544
690 $a 0364
710 2 $a University of Toronto (Canada). $b Electrical and Computer Engineering. $3 2096349
773 0 $t Masters Abstracts International $g 82-01.
790 $a 0779
791 $a M.A.S.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27832781