Algorithm算法代写代考

Numerical Methods & Scientific Computing: lecture notes Root-finding Week 6: aim to cover Numerical linear algebra: Gauss Elimination with Partial Pivoting (GEPP), operations count (Lecture 11) Newton’s method, 2D arrays (matrices) in MATLAB (Lab 6) LU factorization, special matrices (Lecture 12) Numerical Methods & Scientific Computing: lecture notes Linear Systems Trefethen’s Maxims In principle, the

Numerical Methods & Scientific Computing: lecture notes Root-finding Newton’s method slope = f’(xn) y xn+1 y = f(x) based on slope of function xn x Numerical Methods & Scientific Computing: lecture notes Root-finding Derivation Taylor series around xn: f(xn+1)⇡f(xn)+f0(xn)(xn+1 xn)=0 which gives Newton-Raphson iteration: xn+1 = xn f (xn) . f0(xn) Again, a first order

Numerical Methods & Scientific Computing: lecture notes Errors Error propagation Roundo↵ error propagation If roundo↵ error caused by u stayed as big as u ! no problem! Does it? Example Multiplication: (x ⌦ y) ⌦ z ⌘ fl(fl(x ⇥ y) ⇥ z) = [xy(1 + 1)] ⇥ z(1 + 2) where | i |< u

Numerical Methods & Scientific Computing: lecture notes Errors Error propagation Week 5: aim to cover root-finding: bisection, fixed point iteration (Lecture 9) error propagation, bisection, fixed point iteration ( Lab 5) Newton’s method, secant method, fzero (Lecture 10) Numerical Methods & Scientific Computing: lecture notes Root-finding Root-finding methods Findx suchthatf(x)=0 y roots y=f(x) x Numerical

Solution of Week 6 Lab (Prepared by Yuan Yin) December 22, 2019 1 Exercise 1: Newton’s Method: 1. Bysettingf(x)=x2−aandpluggingintox =x − f(xn),weget n+1 n f′(xn) xn2 −a 2xn2 −xn2 +a xn2 xn a xn+1=xn−2x = 2x =2x=2+2x. nnnn This gives the algorithm you coded for Tute2 Exercise1 (e). 2. Try to understand and compare Newton’s

UNIVERSITY OF TORONTO SCARBOROUGH FALL 2020 STAD68 MIDTERM Allowed aids. You may refer to the book when solving these problems. You should not use the internet, any social media platform, or discuss the problems with other students. Point system. Every Question is made up of Parts. (Note that some Questions only have one Part.) All