Use the Cholesky algorithm to find factorization of the form A = LL' for the following matrix 2: Solve the following linear system by Gaussian elimination using double precision of calculator carrying 10 or more digits. Find the approximate X solution using 4-digit arithmetic. Calculate 1 = b - Ax with double precision and find ||r||2 and ||e||2. Is the matrix A conditioned in this case? What can you say considering the condition number? 3.02 -1.05 2.53 4.33 0.56 -1.78 0.83 -0.54 1.447 [4.501 3.11 10.1]
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Step 1: Cholesky factorisation To find the Cholesky factorisation of A, we need to follow these steps: Show more…
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Using a computer with four significant digits with chopping, the Gaussian elimination with partial pivoting solution to the following system: 0.0030x1 + 55.23x2 = 58.12 6.239x1 - 7.123x2 = 47.23 Is: (A) x1 = 26.66; x2 = 1.051 (B) x1 = 8.769; x2 = 1.051 (C) x1 = 8.800; x2 = 1.000 (D) x1 = 8.771; x2 = 1.052 NOTE: Show how you derive the answer using Gaussian elimination and highlight any pivoting that you do.
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