Fall 2002 Math 5660 Review for final

- Given a small square matrix, do Choleski decomposition by hand using outer product Choleski
- the same using inner product Choleski
- Find (and prove!) if a given function (e.g. sqrt(x(1))+sqrt(x(2)) is a norm or not
- Given a small square matrix, compute its spectral radius
- decide if Gauss Seidel iterations for a given matrix converges 
	(use the criterion of diagonal dominance or matrix is symmetric and positive definite)
- decide if Jacobi or Richardson iteration for a given small matrix converges
- given a matrix A size 3 by 3, vectors b and x_0, do one step of the Gauss-Seidel iterative method 
	that is compute x_1 (or SOR with a given omega, or Jacobi)
- given a function f, find a bound on the error of Lagrange interpolation on 3 nodes 
	(also Hermite and Chebychev
- same as above on 2 nodes
- write the interpolation polynomial for a small number of nodes for one of above types, from the definition
- given x_i y_i i=0,1,2 find cubic spline such that s(x_i)=s(y_i), from definition
- given f on [0,1] find n so that the error of piecewise linear interplation of f on equistant nodes 
	x_0=0,...x_n=1 is less than given tolerance in the whole [0,1]
- same for piecewise cubic interpolation using Hermite interpolation on each subinterval 
- Let A and B be square matrices and ||B^{-1}A||<1, write (A+B)^{-1} as Neumann series to show that 
	A+B is regular