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| (x2 + 2y - 1)5/3 | is Math.pow((x*x+2*y-1),5/3) |
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is Math.sqrt(Math.sin(x)/(Math.pow(2,x)+3*Math.log(x))) |
| BISECTION METHOD The root is found by starting with an interval [a, b] that brackets the root. The midpoint, p,is then tested to see if f(p) is of the same sign as f(a) or f(b). Either a or b is then replaced and the interval is bisected - split in half. |
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| FALSE POSITION METHOD The root is found by starting with an interval [a, b] that brackets the root. The secant connecting (a,f(a)) and (b,f(b) is found and its x-axis intercept, p,is then tested to see if f(p) is of the same sign as f(a) or f(b). Either a or b is then replaced and the interval is then shrunk. |
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| SECANT METHOD Two initial estimates p0 and p1 of the root are given. The points on the curve are then connected by a secant. The x-axis intercept is called p2. Next, p1 and p2 are used to produce p3. This method converges more rapidly then the ones above - in fact, it is almost as fast as the Newton-Raphson method but requires fewer function evaluations. There are problems if the first two points are not well chosen. The first two methods are more robust - that is, if [a, b] brackets a single root, then they will always be located by the above two methods for a continuous function. |
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