₦airaland Forum

1. Implement the Bisection method in Matlab and compute the three roots r1, r2 and
r3 of the polynomial P(x) Ξ x2 - 6:83x2 + 12:9682x + 5:358 with an accuracy of five significant digits. In order to create an efficient implementation you should consider the following points:

(a) The roots belong to the following intervals respectively:
r1 ἐ [2:47; 2:58], r2 ἐ [3:71; 3:8], r3 ἐ [0:5; 0:6]

(b) If r is a root of p(x) = 0, then from the polynomial division P(x) Ξ (x-r) q(x) it is clear that the remaining roots of p (x) are those of the quotient q (x). Intuitively the computation of a root of q (x) must in general be faster than the computation of the same root of p (x). This technique is called deflation.

Use (a) to start your computation and (b) to write an efficient program.
2. Explain what benefit you may have in using deflation other than speed, in the case of
Non bracketing methods like Newton are for example.

Do you have matlab on your system? And what sch?