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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2020 • Question 5

Question

Math 6610 • Analysis of Numerical Methods I Spring 2020 • Question 5

Interpolation

Let \(x_0,\ldots ,x_n\) be distinct real points, and consider the following interpolation problem. Choose a function \[ F_n(x)=\sum _{j=0}^{n}a_j e^{jx} \] such that \[ F_n(x_i)=y_i,\qquad i=0,1,\ldots ,n \] with the \(\{y_i\}\) given data. Show there is a unique choice of \(a_0,\ldots ,a_n\).

Raw LaTeX

{Interpolation}

Let \(x_0,\ldots,x_n\) be distinct real points, and consider the following
interpolation problem. Choose a function
\[
  F_n(x)=\sum_{j=0}^{n}a_j e^{jx}
\]
such that
\[
  F_n(x_i)=y_i,\qquad i=0,1,\ldots,n
\]
with the \(\{y_i\}\) given data. Show there is a unique choice of
\(a_0,\ldots,a_n\).

Topic Tags

Linear Programming and Optimization Polynomial Interpolation and Error Formulas