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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2003 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Fall 2003 • Question 6

Spline Spaces Let \(T\) be a triangulation of a domain \(\Omega \), and \(S\) the linear space of functions on \(T\) that are continuous on \(\Omega \) and that on each triangle in \(T\) can be written as a (bivariate) polynomial of degree \(d\). Derive the dimension of \(S\).

Raw LaTeX

{Spline Spaces}
Let \(T\) be a triangulation of a domain \(\Omega\), and \(S\) the linear space of
functions on \(T\) that are continuous on \(\Omega\) and that on each triangle in \(T\) can
be written as a (bivariate) polynomial of degree \(d\). Derive the dimension of \(S\).

Topic Tags

Linear Programming and Optimization Polynomial Interpolation and Error Formulas