Divide the polynomial P4(x)=2x4− 24x3+ 100x2− 168x + 93 by the linear factors (x − z) for z = 1, 2, 3, 4, 5. Write down the calculations using Horner’s scheme (Equation 5.62). What are the remainders r and the resulting coefficients for the polynomial P3(x) in the equation P4(x)=(x − z)P3(x) + r?
We consider again Problem 5.3: find x such that
Since a function evaluation is expensive (summation of the Taylor series) but the derivatives are cheap to compute, a higher order method is appropriate. Solve this equation with Newton’s and Halley’s methods.
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