MCS 471 --- Special Class Notes

Notes from Class on Special Topics

• Floating Point Arithmetic:

  1. Floating Point Problem for Derivatives (HTML).

  2. Professor Hanson's Notes on Basic Floating Point Representation (HTML).

  3. Floating Point References (HTML).

  4. Simple 3 Decimal Digit Floating Point Machine Epsilon MATLAB Example (TXT).

• Integer Arithmetic:
  1. Integer Overflow Reference (HTML).

• Nonlinear Equations:
  1. Secant Method Error and Convergence (PDF)

  2. Zero and Roots Finders Codes with Plots for Class Polynomial Example:
     • MATLAB Demo. Code for Class Polynomial Simple Example (M-File).

     • MATLAB Demo. Code for Class Polynomial More Advanced Example (M-File) .

     • Maple fsolve and plot Demonstration (MWS-File).

  3. Golden Section Search Method for 1-Dim Optimization:

     • Golden Section Search Class Notes (PDF).

     • Golden Section Search Class Numerical Example (TXT).

• Computational Linear Algebra:
  1. Cramer's Rule Computationally Dangerous
     • (HTML?)
     • (PDF?)
  2. Forward Gaussian Elimination with Virtual Row Pivoting and Scaling
     • Sample C-Code with Fortran Notes?
     • Sample C-Code Output for Above?
  3. Newton's Method in n-Dimensions using Forward Gaussian Elimination and Virtual Full Pivoting (HTML)

• Interpolation, Integration and Differential Equations:
  1. Dangers of High Degree Polynomial Interpolation
     • Runge's Counter Example (HTML)
  2. Trapezoidal Rule Class Examples
     • MATLAB Trapezoidal Rule Test Code (M-File)
     • Maple Trapezoidal Rule Test Code and Order of Local Error (MWS)
  3. Gaussian Rule E-Discussion
     • Gaussian Composite Rules (TXT)
     • Gaussian Rule Weight and Node Finding (TXT)