1 / 10

Muller’s Method

Muller’s Method. Dan Heflin Sarah Hare. Muller’s Method. What problem does it solve? How is it r epresented? Where does it come from?. What does Muller’s Method Solve?. It finds the Roots of functions including Complex.

gent
Download Presentation

Muller’s Method

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Muller’s Method Dan Heflin Sarah Hare

  2. Muller’s Method • What problem does it solve? • How is it represented? • Where does it come from?

  3. What does Muller’s Method Solve? • It finds the Roots of functions including Complex. • This method allows the user to find roots for functions that do not have real roots.

  4. How is Muller’s Method Represented?

  5. Where does Muller’s Method Come From? Secant Method Muller’s Method f(xn-1) f(xn) xn-1 xn

  6. Algorithm for Muller’s Method For[i=3,(i<=maxit)&&(Abs[xn1-xn2]<=err),i++, t=(xn-xn1)*(xn-xn2); u=(xn1-xn)*(xn1-xn2); v=(xn2-xn)*(xn2-xn1); If[Abs[t]>0 &&Abs[u]>0&&Abs[v]>0, a= (Y0/t)+(Y1/u)+(Y2/v); b=(-Y0(xn1+xn2)/t)+(-Y1(xn+xn2)/u)+ (-Y2(xn+xn1)/v); c=(Y0 (xn1*xn2)/t)+(Y1 (xn*xn2)/u)+ (Y2 (xn*xn1)/v); r1=(-b+Sqrt[b^2 -4a*c])/(2a); r2=(-b-Sqrt[b^2 -4a*c])/(2a); If[Abs[xn2-r1]<Abs[xn2-r2], xn = xn1; xn1 = xn2; xn2 = r1; Y0 = f[xn]; Y1= f[xn1]; Y2= f[xn2]; ,(*else*) xn = xn1; xn1 = xn2; xn2 = r2; Y0 = f[xn]; Y1= f[xn1]; Y2= f[xn2]; ]; ]; ];

  7. Representation Again

  8. Example

  9. Continued

  10. Continued Since r1 is closer to the actual root of the function, we choose r1 instead of r2. The program continues until the limit of iterations has been met, or the actual root has been found. This is the first iteration of Muller’s Method.

More Related