The course on numerical approximation deals with efficient numerical methods for approximating known or unknown functions of one or multivariables. Mainly, piecewise polynomial functions with certain smoothness are the subject. Both the properties and constructions of these functions will be studied. We first discuss polynomial interpolations, Lagrange and Newton interpolation formulae, Hermite interpolation formula. Difference and divided differences will be introduced. Weierstrass Approximation Theory will be proved. Secondly, we introduce B-splines using divided differences. Various properties of B-splines will be discussed. In particular, the $C^2$ cubic splines will be detailed. Schoenberg-Whitney Theorem will be proved. Thirdly, we discuss Lagrange interpolation in the bivariate setting and introduce splines over triangulations.

In the winter of 1996, I taught this course. The syllabus of this course is here. The course number is MAT834 To see some sample of computer projects, click here.

In the winter of 1997, I taught this course again. The syllabus of this course is here. The course number is MAT834