HW03_short.pdf - Math 104A Homework#3 Instructor Lihui Chai General Instructions Please write your homework papers neatly You need to turn in both full

HW03_short.pdf - Math 104A Homework#3 Instructor Lihui Chai...

This preview shows page 1 - 2 out of 2 pages.

Math 104A Homework #3 * Instructor: Lihui Chai General Instructions: Please write your homework papers neatly. You need to turn in both full printouts of your codes and the appropriate runs you made. Write your own code, individually. Do not copy codes! 1.(a) LetfC2[x0, x1] andP1its interpolation linear polynomial atx0andx1. Prove thatkf-P1k18(x1-x0)2M2,(1)where|f00(x)| ≤M2for allx[x0, x1] andkf-P1k=maxx[x0,x1]|f(x)-P1(x)|.(b) LetP1(x) be the linear polynomial that interpolatesf(x) = sinxatx0= 0 andx1=π/2.Using (a) find a bound for the maximum errorkf-P1kand compare this bound withthe actual error atx=π/4.2.
Image of page 1
Image of page 2

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture