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Math 481a Midterm #1. March 15, 2007
Attention! Please, note that this is the closed book test. You are allowed to use a graphing calculator
(but not a palm). In multiple choice, guessing is not penalized. In other problems, please, show all important
steps in you solution.
1a. (5pt) The Secant method is most closely related to
the bisection method;
the Newton's method;
the Muller's method;
the tangent method;
the Horner's method.
1b. (5pt) In the proof of Theorem 2.3 about the convergence of fixed-point iteration:
Theorem 2.3. Let g C[a, b] be such that g(x) [a, b], for all x in [a, b]. Suppose, in addition, that
g (x) exists on (a, b) and that a constant 0 < k < 1 exists with
|g (x)| k, for all x (a, b).
Then, for any number p0 in [a, b], the sequence defined by
pn = g(pn-1), n 1,