Determine the cholesky factorization

Assignment Help MATLAB Programming

Reference no: EM132915181

Show all your works to receive full credits.

Question 1. Apply two steps of the Newton's method to the equation x³ = 2x + 2 with initial guess x₀ = 1. Show the iterations x₁ and x₂.

Question 2. Consider the function g(x) = x sin x. Find an interval where for each x0, the fixed point iteration x_k = g(x_k-1) always converges to the fixed point x = 0. In the case of convergence, what is the rate of convergence?

Question 3. Consider the matrix,

Determine the Cholesky factorization of A: A = LL^T. Show all you calculations to receive full credits.

Question 4. Suppose that the Gauss-Seidel method is used to solve the linear system, Ax = b, where

What would be the solution after two iterations (x⁽²⁾), assuming that the initial guess is zero (x⁽⁰⁾ = 0)? Will the method converge? Justify your answer.

Reference no: EM132915181

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