Numerical Analysis: Interpolatory Requirement & Coefficient Conditions

[buzzmath]

Homework Statement

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?

Homework Equations

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 won't 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

 

[EnumaElish]

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