Divide the polynomial P4(x)=2x 4 − 24x 3 + 100x 2 − 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...


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.



Jan 05, 2022
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