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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2012 • Question 5

Question

Math 6610 • Analysis of Numerical Methods I Spring 2012 • Question 5

Interpolating Polynomial

Define \(l_{i,n}(x)\) - Lagrange basis functions with \(x_0,x_1,\ldots ,x_n\). Prove that for any \(n\geq 1\), \[ \sum _{i=0}^n l_{i,n}(x)=1 \] for all \(x\).

Raw LaTeX

{Interpolating Polynomial}

\newpage

Define \(l_{i,n}(x)\) - Lagrange basis functions with
\(x_0,x_1,\ldots,x_n\). Prove that for any \(n\geq1\),
\[
  \sum_{i=0}^n l_{i,n}(x)=1
\]
for all \(x\).

\vspace{1.3\baselineskip}

Topic Tags

Linear Programming and Optimization Polynomial Interpolation and Error Formulas