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 Newtons 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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