CAAM 553 · Numerical Analysis I

Fall 2018 · Rice University


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Notes, Software, and Supplementary Material


Lecture Notes: Notes are provided here, with additional links/demos to be posted below.
For help with MATLAB used in the context of numerical analysis, Cleve Moler's book, Numerical Computing with MATLAB may be helpful (available free online).
Lecture 12: Continuous least squares approximation, orthogonal polynomials.
Lecture 19,20 in the course lecture notes.
Suli and Mayers 9.4.
monomial_projection.m: best polynomial approximation using monomials.
legendre_projection.m: best polynomial approximation using orthogonal (Legendre) polynomials.
Lecture 11: Continuous least squares approximation.
Lecture 19,20 in the course lecture notes.
Lecture 10: B-splines.
Lecture 13,14 in the course lecture notes.
Lecture 9: Piecewise polynomial and spline interpolation.
Lecture 13,14 in the course lecture notes.
p1_interp_demo.m showing a comparison between piecewise linear and high order polynomial interpolation.
Lecture 8: Hermite interpolation and error analysis.
Lecture 13,14 in the course lecture notes.
Additional reading: Suli and Mayers 11.
hermite_interp.m showing Hermite interpolation of function and derivative values at equispaced points.
hermite_birkhoff_interp.m showing Hermite interpolation of function and higher derivative values at endpoints.
Lecture 7: Newton bases, Hermite interpolation.
Lecture 13,14 in the course lecture notes.
Additional reading: Suli and Mayers 11.
hermite_interp.m showing Hermite interpolation of function and derivative values at equispaced points.
Lecture 6: Polynomial interpolation: error analysis and Newton bases.
Lecture 10,11 in the course lecture notes.
Additional reading: Suli and Mayers 6.3.
Demo showing convergence of interpolation along with an error bound.
Demo showing growth of derivatives of Runge's function.
Lecture 5: Fixed point iterations. Polynomial interpolation: Lagrange bases and convergence.
Lecture 9, 10 in the course lecture notes.
Additional reading: Suli and Mayers 6.1-6.3.
Demo of Vandermonde matrix and Lagrange form.
Lecture 4: Convergence of the secant method, fixed point iterations.
Lecture 40 in the course lecture notes.
Additional reading: Suli and Mayers 1.1-1.3.
Lecture 3: Root finding: convergence of Newton's method, secant method.
Lecture 39 in the course lecture notes.
Code to compare Secant and Newton's method.
Lecture 2: Root finding: bisection and Newton's method.
Piazza forum signup.
Lectures 38,39 in the course lecture notes.
Additional reading: Suli and Mayers 1.4, 1.6.
Matlab demo
Lecture 1: Introduction to Numerical Analysis:
Floating point number systems, catastrophic cancellation.
Rounding error disasters
Lectures 1,8 in the course lecture notes.