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Sekantmetoden

Sekantmetoden. y. Sekantmetoden. Y=f(x). S. x. x*. x k+1 x k x k-1. Newton-Raphson. y. Newton-Raphsons metode. y = f(x). L. x. x *. x k+1 x k. Bisektion. y. Bisektion Beregn x k = (y k + z k )/2 og f(x k ) 2a) Hvis f(x k ) = 0, så stop.

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Sekantmetoden

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  1. Sekantmetoden y Sekantmetoden Y=f(x) S x x* xk+1 xk xk-1

  2. Newton-Raphson y Newton-Raphsons metode y = f(x) L x x* xk+1 xk

  3. Bisektion y • Bisektion • Beregn xk = (yk + zk)/2 og f(xk) • 2a) Hvis f(xk) = 0, så stop. • 2b) Hvis f(xk)f(yk) > 0, så sæt • yk+1 = xk og zk+1 = zk • 2c) Hvis f(xk)f(yk) < 0, så sæt • yk+1 = yk og zk+1 = xk y = f(x) yk xk x zk

  4. Invers kvadratisk konvergens Approksimation af kvadratisk polynomium y y = f(x) x xk xk-1 xk-2 Når y sættes = 0 findes xk+1 således: Kilde: http://www.ii.uib.no/~anto/i162/Slides/Forel9pv.pdf

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