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Homework Help: Numerical analysis

  1. Dec 3, 2007 #1
    1. The problem statement, all variables and given/known data
    take the rational function R(x)=(a+bx)\(c+dx). What does the interpolatory requirment R(xi)=yi, i=1,2,3,4 amount to? under what conditions can you find coefficients? uniquely?

    2. Relevant equations

    3. The attempt at a solution
    Let y=[y1,y2,y3,y4] and v=[a,b,c,d] and let A be an 4x4 matrix. then I want to try to write this as Av=y and the solution would would exist and be unique when A is invertible. so I write a+bxi=(c+dxi)yi. then I can write a+bxi-cyi-d(xi)(yi)=0 but this wont give me the solution because we could just write a=b=c=d=0 for any x and y. since I know yi and xi I could have a+bxi-cyi = d(xi)(yi) and set up the matrix that way but it still won't give me what I want since I wouldn't be able to find d. Am I on the right track? any suggestions on where to go from here? thanks
  2. jcsd
  3. Dec 3, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    In A you have 16 matrix elements, but Av = y corresponds to only 4 equations. You need 12 more equations for a unique solution.
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