hw2 - Homework 2 Math 104A Winter 2009 Due on Wednesday January 21st 2009 Section 2.1 6 12 14 16 and 20 Section 2.2 1 2 3 4 11.a 11.b 11.c and 23

# hw2 - Homework 2 Math 104A Winter 2009 Due on Wednesday...

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Homework 2 – Math 104A, Winter 2009 Due on Wednesday, January 21st, 2009 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 * ) = 0, then g ( x * ) = 0. Deduce from this that the convergence of Newton’s method is quadratic, i.e., if we denote by