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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2019 • Question 5

Question

Math 6610 • Analysis of Numerical Methods I Fall 2019 • Question 5
**Interpolation** **a)** State the theorem about the existence and uniqueness of interpolating polynomial. Give a proof. (You can consider any proof of your choice). **b)** Let \(f(x)=x^2+5x+1\). Find the polynomial of degree 3 that interpolates the values of \(f\) at \(x=-1,0,1,2\).

Raw LaTeX

{Interpolation}

\partitem{a} State the theorem about the existence and uniqueness of
interpolating polynomial. Give a proof. (You can consider any proof of your
choice).

\partitem{b} Let \(f(x)=x^2+5x+1\). Find the polynomial of degree 3 that
interpolates the values of \(f\) at \(x=-1,0,1,2\).

\newpage

Topic Tags

Linear Programming and Optimization Polynomial Interpolation and Error Formulas