hw1 - , 1]: (i) f ( x ) = x 3 ; (ii) f (1 / 2) = 1 ,f ( x )...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 128a, fall 2011, Chorin, theory homework 1, due in the week of Sept. 5. 1. Use the formula for the error in interpolation to show that if two polyno- mials P n ,Q n of degree n coincide at n +1 distinct points, then they are identical and coincide at all points. 2. Suppose you represent the function f ( x ) = e x in the interval [0 , 3] by the first 7 terms of its Taylor series. Find a bound for the difference between f and the sum of these terms in that interval. 3. Find the maximum norm of the following functions on the interval [0
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , 1]: (i) f ( x ) = x 3 ; (ii) f (1 / 2) = 1 ,f ( x ) = 0 when x 6 = 1 / 2. (iii) f ( x ) =-x 100 . 4. Find the least squares norm of each of the functions in the previous prob-lem. 5. Consider the function f ( x ) = x n , where n is a positive integer; find its maximum norm and its least squares norm. Find what happens to these norms as n → ∞ . 1...
View Full Document

This note was uploaded on 01/21/2012 for the course MATH 128A taught by Professor Rieffel during the Fall '08 term at University of California, Berkeley.

Ask a homework question - tutors are online