Evaluate the convergence of the algorithms, Mathematics

Assignment Help:

Evaluate the convergence of the algorithms:

From the convergence proof of power method, LR and QR algorithm for the computation of eigenvalues we see that the easiest case to proof convergence of these algorithms is when all eigenvalues of a matrix are distinct and their absolute values are also distinct.

Conversely, it is not difficult to imagine that the convergence can be difficult to obtain when several eigenvalues have similar absolute values or in the case of repeated eigenvalue. In this project, we attempt to examine some of these more challenging cases.

Algorithmic Analysis

(a) Show that for any real valued matrix A, if a complex number is an eigenvalue, the complex conjugate μ must also be an eigenvalue.

(b) Consider a matrix A with a complex eigenvalue with non-zero imaginary part. Consider the Jornal canonical form of matrix A obtained via similarity transformation. What are the relationships between elementary Jordan blocks associated with and ?

(c) When using the power method or the LR or QR algorithm, can the algorithm converge to an upper-triangular matrix?

(d) Propose a possible approach to compute complex eigenvalues of a real valued matrix A.

Computer Implementation

(a) Implement LR and QR for computation of eigenvalues including algorithm to first transform the input matrix to a Henssenberg matrix.

(b) Validate the correctness of your implementation.

(c) Evaluate the convergence of the algorithms in the case of matrix with complex eigenvalue.


Related Discussions:- Evaluate the convergence of the algorithms

Evaluate performance of mental arithmetic maths, E 1) Try the two activitie...

E 1) Try the two activities detailed above with a few children around you Evaluate whether they really helped to improve the children's performance of mental arithmetic. Anot

LPP, howto know whether a region is bounded or not

howto know whether a region is bounded or not

Find the maximum and minimum brightness values, Variable stars are ones who...

Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.

MENSURATION, HOW TO FIND THE HEIGHT OF A CYLINDER I NEED IT FOR ASSIGNMENT ...

HOW TO FIND THE HEIGHT OF A CYLINDER I NEED IT FOR ASSIGNMENT TO BE SUBMITTED BY 8;00 AM

Computing limits , Computing Limits :In the earlier section we saw that t...

Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi

Determine the nand gate, Find out the two inputs when the NAND gate output ...

Find out the two inputs when the NAND gate output will be low. Ans. The output of NAND gate will be low if the two inputs are 11. The Truth Table of NAND gate is shown

Mensuration, In an equilateral triangle 3 coins of radius 1cm each are kept...

In an equilateral triangle 3 coins of radius 1cm each are kept along such that they touch each other and also the side of the triangle. Determine the side and area of the triangle.

Decimals, how do u add them together?

how do u add them together?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd