hw2 - Homework 2 Math 104A Fall 2010 Due on Tuesday October...

This preview shows page 1 out of 1 page.

Homework 2 – Math 104A, Fall 2010 Due on Tuesday, October 12th, 2010 Section 2.1: 6, 12, 14, 16, and 20. Section 2.2: 1, 2, 3, 4, 11.a, 11.b, 11.c, and 23. Additional problem: Consider the iteration in Newton’s method: p n +1 = g ( p n ) where g ( x ) = x f ( x ) f ( x ) Prove that if f ( x ) = 0, and f ( x ) negationslash = 0, then g ( x ) = 0. Deduce from this that the convergence of Newton’s method is quadratic, i.e., if we denote by
Image of page 1

Unformatted text preview: e n the error of the n-th approximation ( e n = p n − x ∗ ), then e n +1 ≤ Ke 2 n for some K > 0, as long as the initial iterate p is suFciently close to x ∗ . You may assume that f has in±nitely many continuous derivatives. 1...
View Full Document

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern