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Welcome to the MATH5315 wiki!

This is just a simple page to explain what the contents of each folder is, since it is pretty vaguely named.

Files

hw1

This homework is a simple check of understanding for rates of convergence and float point errors.

• prob5.py was written to compare rates of convergence.
• prob6.py was written to determine machine epsilon, xmin, and xmax in both single and double precision.

hw2

This homework is focused on Nonlinear Solvers.

• aitken_fp.py implements an Aitken Extrapolation.
• fixed_point.py implements a standard Fixed Point Iteration.
• newton.py implements a scalar-valued Newton's Method (Newton–Raphson method)
• steffensen.py implements a scalar-valued Steffensen's Method.
• prob3.py is a testing file to race Newton's Method v. Steffensen's Method.
• prob4.py is a testing file to compare a standard fixed point iteration to an Aitken Extrapolation.

hw3

This homework is focused on Interpolation.

• quadratic_sol.py is a root finder I designed to use polynomial interpolation to do root finding.
• prob2.py is a testing file to race my solver against Newton's Method and Steffensen's Method.
• newton.py implements a scalar-valued Newton's Method (Newton–Raphson method)
• steffensen.py implements a scalar-valued Steffensen's Method.

hw4

This homework is focused on Cubic Spline Interpolation.

• cubic_spline.py contains functions to build and evaluate a cubic spline with certain boundary conditions.
• Runge_spline_test.py is a testing file to create and plot the results of a cubic spline interpolating the 1D Runge function.