# Ch4_4 - Next Previous Section 4.4 Root Finding I Section...

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Unformatted text preview: Next Previous Section 4.4: Root Finding I Section 4.4: Root Finding I 11 ® Analytical ® Successive substitution ® Bisection ® Section 4.5 Root finding II ® Newton’s method ® Secant method Section 4.4: Root Finding I Next Previous Section 4.4: Root Finding I Section 4.4: Root Finding I 22 ® Linear ® f(x) = ax + b ® f(x) = 0 E xroot = -b/a ® Quadratic ® f(x) = ax2 + bx + c ® f(x) = 0 ™ xroot = {-b (+/-)sqrt(b2-4ac)}/2a ® Cubic and higher ® f(x) = ax3 + bx2 + cx + d ® f(x) = 0 & no simple equation The form of the equation is important Next Previous Section 4.4: Root Finding I Section 4.4: Root Finding I 33- 15- 10- 5 5 10 15- 10- 5 5 10 f(x) x x = -1.41, +4.74 x = 5 Example functions f(x) = 0.18x3 - 0.5x2 - 2x + 1 f(x) = -0.3x2 + x + 2 f(x) = x - 5 Next Previous Section 4.4: Root Finding I Section 4.4: Root Finding I 44 ® Solve for highest order x ® f(x) = 0.18 x 3 - 0.5x2 - 2x + 1 ® x calc = [(0.5x2+2x-1)/0.18] 0.33333 ® Guess an initial value for x, calculate x calc ® use x calc as x,…etc....
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Ch4_4 - Next Previous Section 4.4 Root Finding I Section...

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