Math 481: Objectives for Midterm Exam

Describe the precision and magnitude range of the IEEE long precision binary floating point format.
Explain how the floating point representation fl(x) of a real number x is determined, and find fl(x) for 'simple' numbers x.
Use the concepts of absolute error and relative error, and compute them in specific cases.
Recognize computations that lead to loss of significance, and find remedies for them.
Distinguish between well-conditioned and ill-conditioned problems.
Distinguish between stable and unstable algorithms.

Construct and use an interpolating polynomial in both Lagrange form and Newton divided difference form.
Compute divided difference tables, and use the Hermite-Genocchi formula to interpret the entries.
Use the interpolation error formula.

State the conditions for a linear spline interpolant; for an interpolating cubic spline.
Identify different kinds of cubic splines according to end conditions.
Set up equations for cubic spline coefficients, and use the diagonally dominant tridiagonal matrix algorithm to solve them.

Find the least squares polynomial approximation of a function by using the normal equations.
Use orthogonal polynomials to find the least squares polynomial approximation of a function.