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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.
Euler''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
5-4
Solve the subsequent IVP and find the interval of validity for the solution. y' + (4/x) y = x 3 y 2 , y(2) = - 1, x > 0 Solution Thus, the first thing that we re
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What do we mean by the roots of a quadratic equation ?
how to make a venn diagram?
What percent of the figure below is shaded? Break the rectangle into eighths as shown below. The shaded part is 6/8 or 3/4 ; 3/4 is 75%.
New England University maintains a data warehouse that stores information about students, courses, and instructors. Members of the university's Board of Trustees are very much inte
solve x+y= 7 and x-y =21
50387 divided by 21
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