University of Minnesota
CSci 5302 - Analysis of Numerical Algorithms
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CSCi 5302 - Spring 2020 -- Course Schedule

Last Revised 01/14/20 (provisional schedule, dates subject to change)

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WEEK DATE TOPICS
1 1/22 Scientific Computing - Goals and Fundamentals (Chap 1)
  • floating point arithmetic
  • relative error
  • conditioning vs stability: backward error vs forward error
  • truncation error vs rounding error.
2 1/27 Scalar Nonlinear Equs (Chap 5, secs 1, (2), 4 ?)
  • Existence and Uniqueness
  • Sensitivity and Conditioning. backward error vs forward error
  • Methods: Bisection, Newton, Secant.
  • HW1 due Wed Jan 29
3 2/03 ... Nonlinear equations continued
  • General Fixed Point Methods.
  • Convergence Rates and Stopping Criteria
... ... Systems of Linear Equations (Chap 2, secs 1-4, up to 2.4.7)
  • Existence and Uniqueness
  • Norms.
4 2/10 ... Linear equations continued
  • Sensitivity and Conditioning.
  • Methods: Gaussian Elimination and Back Substitution.
  • HW2 due Mon Feb 10.
5 2/17 Nonlinear Equations -- Systems (Chap 5, secs 4-6)
  • Partial Derivatives: gradients, Jacobians.
  • Fixed Point Methods. Newton's method.
6 2/24 MIDTERM I (on Monday, in class).
6 2/24 Polynomial Interpolation (Chap. 7, secs 1-3)
  • Existence and Uniqueness
  • Methods: undetermined coefs.
7 3/02 ... Interpolation continued
  • Methods: Lagrange polynomials. divided differences.
... ... Splines (Chap 7. sec 4)
  • Piecewise polynomial interpolation: splines.
  • Two-dimensional interpolation/splines (from notes).
  • HW3 due Mon Mar 02.
8 3/09 Linear Least Squares (Chap 3, secs 1, 2)
  • Existence and Uniqueness
  • Normal equations.
  • Projections.
... ... Unconstrained Optimization Problems (Chap 6, esp. secs 1-5)
  • Existence and Uniqueness: coercive and convex functions
  • Conditioning
  • First & second order conditions for optimality in 1D, gradients, Hessians.
  • One-dimension: Golden Section Search.
=== 3/15 Spring Break
  • Romp in the sand or the snow.
9 3/23 ... Unconstrained Optimization continued (multi-dimensional)
  • First & second order conditions for optimality (multi-dim): gradients, Hessians.
  • Conditioning
  • Multi-dimensional methods: steepest descent, Newton, BFGS.
  • Line Search
  • HW4 due Mon Mar 23.
10 3/30 Constrained Optimization Problems (Chap 6, sec 7)
  • Equality constraints, inequality constraints
  • First Order conditions for optimality: KKT conditions
11 4/06 MIDTERM II (on Monday, in class).
11 4/06 Constrained Optimization Problems (Chap 6, sec 7)
  • Penalty & barrier methods. (maybe dual ascent methods?)
  • Linear Programs.
12 4/13 Numerical Integration and Quadrature (Chap 8, secs 1-4,7)
  • Existence and Uniqueness
  • Numerical Quadrature (equally-spaced points).
  • Adaptive Quadrature
  • Richardson Extrapolation: Romberg.
  • HW5 due Mon Apr 13.
13 4/20 Initial Val. Probs. for Ord. Diff. Equs
  • Existence and Uniqueness, stability of solutions
  • Linear ODEs
  • Methods: Euler, Backward Euler.
14 4/27 ... ODEs continued
  • Accuracy and Stability: local vs global truncation error
  • Runge-Kutta Methods
  • HW6 due Mon Apr 27.
15 5/04 MIDTERM III (on Monday, in class).

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