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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.
Functional and variations.Block III, Consider the functional S[y]=?_1^2 v(x^2+y'')dx , y(1)=0,y(2)=B Show that if ?=S[y+eg]-S[y], then to second order in e, ?=1/2 e?_1^2¦?g^'
34+8-76=
How should shoppers Stop develop its demand forecasts?
Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin
From top of a tower a stone is thrown up and it reaches the ground in time t1. A second stone is thrown down with the same speed and it reaches the ground in t2. A third stone is r
Evaluate following limits. Solution : Let's do the first limit & in this case it sees like we will factor a z 3 out of the numerator and denominator both. Remember that
6987+746-212*7665
the wholesale p of string beans in dollars per bushel and the daily supply x in thousands of bushel,are related by the equation px+6x+7p=5950. if the supply is decreasing at the r
An irregular perimeter to the circumference of a circle such as a protrusion
This problem involves the question of computing change for a given coin system. A coin system is defined to be a sequence of coin values v1 (a) Let c ≥ 2 be an integer constant
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