False Position Method notes

False Position Method notes - False-position method Basic...

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Basic idea Similar to Secant method Different from secant method is that it has an extra condition to ensure the root is bracketed between iteration when finding the next secant line. Starting with x i and x i+1 , using the secant formula we can find x i+2 . For secant method, we use x i+2 and x i+1 for the next approximation. In fact, we have another choice 1) x i+2 joining with x i+1 (secant method) 2) x i+2 joining wiht x i The method of false position provides an extra condition False-position method
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Fig. 6.8 f(x i+1 ) x i+1
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F(x i+2 )*F(x i+1 ) < 0 Bracketing condition Yes X i+2 = x i+2 X i+1 = x i+1 No X i+2 = x i+2 X i+1 = x i Used in the recursive formula to find the next secant line or approximation The added insurance commonly requires more iterations than the secant method Swap False-position method
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An example 0 3 3 2 3 = + x x x 3 = r -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -5 -4 -3 -2 -1 0 1 2 3
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1 1.5714 2 1.5714 NA 0.0927 2
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False Position Method notes - False-position method Basic...

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