Lecture Topics in 421, Fall 98

• Wed Sept 9 intro, Matlab, interpretation of matrix*vector, plotting sum of sines
• Mon Sept 14 more on Matlab, plots, random numbers, pi
• Wed Sept 16 IEEE representation: single and double, special representation of zero, subnormals, inf and NaN
• Mon Sept 21 IEEE representation: use of inf in parallel resistance formula, and 2 while loop programs: (1) while loop dividing x by 2 until x underflows to 0, and (2) while loop dividing x by 2 until 1+x equals 1 (big difference in termination - make sure you understand why)
• Wed Sept 23 The Intel Floating Point Register stack. FPL: Floating Point Lab, illustrating the Intel processor and IEEE representation. Students are encouraged to get a copy of FPL from me.
• Mon Sept 28 finite difference approx of derivative: how big should h be? The very different roles of truncation error and rounding error.
• Wed Sept 30 myexp: computing an exponential. The difference between absolute and relative error. Vandermonde system of equations for polynomial interpolation.
• Mon Oct 5 Why relative error measures the number of "correct digits" (review of myexp). Horner's rule to evaluate a polynomial, repeat of how to set up and solve Vandermonde system to get the polynomial coefficients and plot the polynomial. See InterpV, HornerV.
• Wed Oct 7 Newton form of interpolating polynomial (Chap 2.2). InterpNRecur (recursive implementation) HW3 assigned.
• Mon Oct 12 Went over HW 1 and 2. Briefly did: Horner's rule for the Newton form of interpolating polynomial: HornerN.
• Wed Oct 14 QUIZ and answers to quiz.
• Mon Oct 19 Briefly: Newton form of interpolating polynomial again: InterpN (nonrecursive implementaton). Piecewise Polynomial Interpolation (Chap 3.1), including piecewise cubic Hermite interpolation (Chap. 3.2). Looked at many codes in Chapter 3, including HCubic (cubic Hermite interpolation on one interval).
• Wed Oct 21 The error in the interpolating polynomial (Theorem 2). Reviewed cubic Hermite interpolation. HW4 assigned.
• Mon Oct 26 MIDTERM
  
  
• Wed Oct 28 Linear Systems of Equations: Tridiagonal and Triangular
  
  
• Mon Nov 2 Cubic Splines
  
  
• Wed Nov 4 Cubic Splines
  
  
• Mon Nov 9 Gauss Elimination
  
  
• Wed Nov 11 Singular Matrices and Redundant/Inconsistent Equations
  
  
• Mon Nov 16 Fast Fourier Transform (Madhu)
  
  
• Wed Nov 18 Strassen Matrix Multiplication (Madhu)
  
  
• Mon Nov 25 The Conditioning of a Matrix - how to measure how nearly singular a matrix is, and limits on computed accuracy of Ax=b
  
  
• Wed Nov 27 Bisection and Newton Methods to solve a Nonlinear Equation
  
  
• Mon Nov 30 Quadratic Convergence of Newton's Method
  
  
• Wed Dec 2 Euler's Method for Solving a Differential Equation
  
  
• Mon Dec 7 More on Differential Equations
  
  
• Wed Dec 9 More on Differential Equations
  
  
• Mon Dec 14 Last Lecture
  
  Attendance at all lectures is REQUIRED. If you are unable to attend, you must send me an email with an explanation.
  
  not done yet: Correctly Rounded Arithmetic (Notes on Floating Point, starting p.26).