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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.
what is the least number of faces and bases the paperweight could have?
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Use an appropriate infinite series method about x = 0 to find two solutions of the given differential equation: y''''-xy''-y=0
Continuous Uniform Distribution Consider the interest earned on a bank deposit. Let X equal the value after the decimal point. (Assume no rounding off to the nearest paise.) Fo
I need help solving principal equations where interest,rate,and time are given.
how to explain this strategy? how to do this strategy in solving a problem? can you give some example on how to solve this kind of strategy.
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How do I solve this problem: Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle th
An engineer has 200 resistors that he keeps in one box. Resistors are colored to help their identification, and in this box there are 30 white resistors, 50 black resistors, 80 red
37x7= multiply answer it.
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