AAE-NA-Labs/01_Direct-Methods-for-Solving-Linear-Systems/Report/problems/Problem13.tex

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2023-03-11 20:08:05 +01:00
\subsection{Problem 13}
Let $\mathbf{Ax = b}$ , where $A = I_N \bigotimes C^TC$, the symbol $\bigotimes$ denotes the Kronecker product, $I_N \in R^{N \times N}$ is an identity matrix, $C \in R^{M \times M}$ is a random matrix with a uniform distribution, $M = 100$, and $N=50$, and $x \square N(0, I_{MN})$. Find the direct method that solves the above system of linear equations with the lowest computational cost. Estimate the cost with a roughly calculated number of flops and with the elapsed time.