Exam (elaborations)
Numerical Analysis
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Taylor's Theorem with Remainder - Fixed Point Convergence - If g is continuously differentiable, g(r)=r, and ‖g'(r)‖<1, then the fixed point iteration converges linearly with rate S to the fixed point r. S=‖g'(r)‖ Newton's Method - Approximates the root of non-linear functions by finding the root of the tangent line. In the second iteration, plug in the approximation from the first iteration as "x_n". Repeat recursively. Newton's Method Convergence - Newton's Method converges quadratically to a root x if f'(r)≠0 at rate M. M=lim(e_(i+1))/e_i² Derivation of Newton's Method - f'(x_0)(x-x_0)=0-f(x_0) x-x_0=-f(x_0)/f'(x_0)
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Numerical Analysis
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Numerical Analysis
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