Unformatted text preview: g ( x ), we know that the error of the n-th iterate satisﬁes e n = x n-p = g ( x n-1 )-g ( p ) . We saw in class that if g ( p ) = 0 and g 00 ( x ) is continuous at x = p , the iteration converges quadratically. State conditions under which one can expect an iteration to converge cubically. 8. Prove: If f ( x ) is a polynomial of degree ≤ n , then the polynomial of degree ≤ n which interpolaties f ( x ) at x , x 1 , . . . , x n is f ( x ) itself. 9. A table of values of cos x is required so that linear interpolation will yield six decimal-place accuracy for any value of x in [0 , π ]. Assuming that the tabular values are to be equally spaced, what is the minimum number of entries needed in the table? 1...
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This note was uploaded on 12/26/2011 for the course MATH 104a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08