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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.
In traveling three-fourths of the way around a traffic circle a car travels 0.228 mi. What is the radius of the traffic circle? The radius of the traffic circle is ____ mi.
using v=g/k(1-e^-kt) find the velocity of the skydiver when k is 0.015
solve the recurrence relation an=2an-1+n, a0=1
A 64-ounce bottle of detergent costs $3.20. What is the cost per ounce of detergent? To ?nd out the cost per ounce, divide the cost through the number of ounces; $3.20 ÷ 64 =
evaluate the expression a) 10C4 b) 10P4.....I do not understand this
The Addition Rule: Mutually Exclusive Events P(A or B or C) = P(A) + P(B) + P(C) This can be represented by the Venn diagram as follows:
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
what are the parts of angles
Give an example of Divisibility? If you can divide one number by another without getting a remainder, we say that the first number is divisible by the second. For instance, the
The function A(t) = 5(0.7)^t was used to define the amount A in milliliters of a drug in the bloodstream t hours after the drug was ingested. Determine algebraically the time it wi
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