The Elements of Eigenvalue and Eigenvector Theory

1998 ◽  
pp. 227-265
Author(s):  
Larry Smith
Keyword(s):  
Eigenvalue And Eigenvector

Computing the Maximal Eigenvalue and Eigenvector of a Positive Matrix

1968 ◽  
Vol 5 (2) ◽  
pp. 269-274 ◽  
Author(s):  
C. A. Hall ◽  
T. A. Porsching
Keyword(s):  
Maximal Eigenvalue ◽  
Positive Matrix ◽  
Eigenvalue And Eigenvector

Refined Algorithm for Solving High-Order Harmonics of Multi Group Neutron Diffusion Equation

2017 ◽  
Author(s):  
Gaoxin Zhou ◽  
Zhi Gang
Keyword(s):  
Diffusion Equation ◽  
Iteration Method ◽  
Krylov Subspace ◽  
Krylov Subspace Method ◽  
Neutron Diffusion ◽  
Subspace Method ◽  
Arnoldi Method ◽  
Arnoldi Algorithm ◽  
Eigenvalue And Eigenvector ◽  
Neutron Diffusion Equation

In recent years, high order harmonic (or eigenvector) of neutron diffusion equation has been widely used in on-line monitoring system of reactor power. There are two kinds of calculation method to solve the equation: corrected power iteration method and Krylov subspace methods. Fu Li used the corrected power iteration method. When solving for the ith harmonic, it tries to eliminate the influence of the front harmonics using the orthogonality of the harmonic function. But its convergence speed depends on the occupation ratio. When the dominant ratios equal to 1 or close to 1, convergence speed of fixed source iteration method is slow or convergence can’t be achieved. Another method is the Krylov subspace method, the main idea of this method is to project the eigenvalue and eigenvector of large-scale matrix to a small one. Then we can solve the small matrix eigenvalue and eigenvector to get the large ones. In recent years, the restart Arnoldi method emerged as a development of Krylov subspace method. The method uses continuous reboot Arnoldi decomposition, limiting expanding subspace, and the orthogonality of the subspace is guaranteed using orthogonalization method. This paper studied the refined algorithms, a method based on the Krylov subspace method of solving eigenvalue problem for large sparse matrix of neutron diffusion equation. Two improvements have been made for a restarted Arnoldi method. One is that using an ingenious linear combination of the refined Ritz vector forms an initial vector and then generates a new Krylov subspace. Another is that retaining the refined Ritz vector in the new subspace, called, augmented Krylov subspace. This way retains useful information and makes the resulting algorithm converge faster. Several numerical examples are the new algorithm with the implicitly restart Arnoldi algorithm (IRA) and the implicitly restarted refined Arnoldi algorithm (IRRA). Numerical results confirm efficiency of the new algorithm.

scholarly journals An instrumental orchestration for online course at the university level

Apertura ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 22-37
Author(s):  
José Orozco-Santiago ◽  
◽  
Carlos Armando Cuevas-Vallejo ◽  
Keyword(s):  
Mathematics Education ◽  
Engineering Students ◽  
Dynamic Geometry ◽  
Dynamic Geometry Environment ◽  
Synchronous Mode ◽  
Instrumental Orchestration ◽  
Video And Audio ◽  
The University ◽  
Eigenvalue And Eigenvector ◽  
Online Mathematics

In this article, we present a proposal for instrumental orchestration that organizes the use of technological environments in online mathematics education, in the synchronous mode for the concepts of eigenvalue and eigenvector of a first linear algebra course with engineering students. We used the instrumental orchestration approach as a theoretical framework to plan and organize the artefacts involved in the environment (didactic configuration) and the ways in which they are implemented (exploitation modes). The activities were designed using interactive virtual didactic scenarios, in a dynamic geometry environment, guided exploration worksheets with video and audio recordings of the work of the students, individually or in pairs. The results obtained are presented and the orchestrations of a pedagogical sequence to introduce the concepts of eigenvalue and eigenvector are briefly discussed. This work allowed us to identify new instrumental orchestrations for online mathematics education.

24.—Eigenvalue and Eigenvector Solutions of a Wave System in a Non-Linear Dissipative Medium

1972 ◽  
Vol 70 ◽  
pp. 251-261
Author(s):  
M. A. S. Ross ◽  
D. F. Corner
Keyword(s):  
Boundary Layer ◽  
Numerical Methods ◽  
Flat Plate ◽  
Stability Theory ◽  
Plate Boundary ◽  
Second Order ◽  
Wave System ◽  
Dissipative Medium ◽  
Eigenvalue And Eigenvector ◽  
Flat Plate Boundary Layer

SynopsisThis paper gives an account of some numerical methods which have been applied to solve the equations of second order stability theory in the flat plate boundary layer.

Eigenvalue of Intuitionistic Fuzzy Matrices Over Distributive Lattice

2019 ◽  
Vol 8 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Amal Kumar Adak ◽  
Ezzatallah Baloui Jamkhaneh
Keyword(s):  
Distributive Lattice ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Matrix ◽  
Intuitionistic Fuzzy ◽  
Eigenvalue And Eigenvector

In this article, the concepts of intuitionistic fuzzy complete and complete distributive lattice are introduced and the relative pseudocomplement relation of intuitionistic fuzzy sets is defined. The concepts of intuitionistic fuzzy eigenvalue and eigenvector of an intuitionistic fuzzy matrixes are presented and proved that the set of intuitionistic fuzzy eigenvectors of a given intuitionistic fuzzy eigenvalue form an intuitionistic fuzzy subspace. Also, the authors obtain an intuitionistic fuzzy maximum matrix of a given intuitionistic fuzzy eigenvalue and eigenvector and give some properties of an intuitionistic fuzzy maximum matrix. Finally, the invariant of an intuitionistic fuzzy matrix over a distributive lattice is given with some properties.

scholarly journals Eigenvalue and eigenvector statistics in time series analysis

2020 ◽  
Vol 129 (6) ◽  
pp. 60003
Author(s):  
Paolo Barucca ◽  
Mario Kieburg ◽  
Alexander Ossipov
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Series Analysis ◽  
Eigenvalue And Eigenvector

A New Close-Form Solution for Initial Registration of ICP

2010 ◽  
Vol 143-144 ◽  
pp. 287-292
Author(s):  
Li Zhao Liu ◽  
Xiao Jing Hu ◽  
Yu Feng Chen ◽  
Tian Hua Zhang ◽  
Mao Qing Li
Keyword(s):  
Closed Form Solution ◽  
Goal Function ◽  
Form Solution ◽  
Initial Value ◽  
Global Goal ◽  
Online Matching ◽  
Testing Algorithm ◽  
Close Form ◽  
Eigenvalue And Eigenvector ◽  
The Relationship

The paper proposed a original matching algorithm using the feature vectors of rigid points sets matrix and a online matching intersection testing algorithm using the bounding sphere. The relationship searching between points in each set is took place by the corresponding eigenvectors that is a closed form solution relatively. The affine transformed eigenvalue and eigenvector is also used instead of the affine transformed points sets for the non-rigid matching that do not need the complicated global goal function. The characteristics matching for the initial registration can give a well initial value for the surfaces align that improve the probability of global solution for the following-up ICP

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