MATH 435
Spring 2009 Prof. B. Datta
Homework #2
Due: February 13, 2009
1. The polynomial P8(x) = x8+ 2x7+x6+ 2x5+ 5x3+ 7x2+ 5x+ 7 has a pair of
complex-conjugate zeros x=±i. Approximate them using Muller’s method. (Do
three iterations) Choose x0= 0, x1= 0.1, x2= 0.5.
2. The polynomial P6(x)=3x6−7x3−8x2+ 12x+ 3 = 0 has a double root at x=−1.
Approximate this root first by using standard Newton’s method and then by two
modified Newton’s methods, starting x0=−0.5.
Use Horner’s method to find the polynomial value and its derivative at each iteration.
Present your results in tabular form. (Do three iterations.)
3. Starting with x0= 0, and x1= 0.5, generate a set of approximations {x2, . . . , xk, xk+1 , . . .}
until |xk+1 −xk|<0.0005 to find a zero of f(x) = tan(x)−x, based on fixed point
iteration. Then compute {ˆxk}using Aitken’s acceleration scheme. Compare how con-
vergence is improved. Check if the convergence is improved by Aitken’s scheme if
Newton’s method is used in place of fixed-point iteration.
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