University of Minnesota
CSci 5302 - Analysis of Numerical Algorithms
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CSCi 5302 - Spring 2019 -- Course Schedule

Last Revised 01/14/19 (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 1/29 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 Jan 29
3 2/05 ... 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 2/12 ... Linear equations continued
  • Sensitivity and Conditioning.
  • Methods: Gaussian Elimination and Back Substitution.
5 2/19 Nonlinear Equations -- Systems (Chap 5, secs 4-6)
  • Partial Derivatives: gradients, Jacobians.
  • Fixed Point Methods. Newton's method.
  • HW2 due Feb 19.
6 2/26 Polynomial Interpolation (Chap. 7, secs 1-3)
  • Existence and Uniqueness
  • Methods: undetermined coefs.
6 2/28 MIDTERM I (on Thursday, in class).
7 3/05 ... Interpolation continued
  • Methods: Lagrange polynomials. divided differences.
... ... Splines (Chap 7. sec 4)
  • Piecewise polynomial interpolation: splines.
  • Two-dimensional interpolation/splines (from notes).
8 3/12 Linear Least Squares (Chap 3, secs 1, 2)
  • Existence and Uniqueness
  • Normal equations. Projections.
  • Orthogonal Transformations. Gram-Schmidt.
  • HW3 due Mar 12.
=== 3/18 Spring Break
  • Romp in the sand or the snow.
9 3/28 Unconstrained Optimization Problems (Chap 6, esp. secs 1-5)
  • Existence and Uniqueness: coercive and convex functions
  • Conditioning
  • First & second order conditions for optimality, gradients, Hessians.
10 4/02 ... Uncontrained Optimization continued (methods)
  • One-dimension: Golden Section Search.
  • Multi-dimensional methods: steepest descent, Newton, BFGS.
  • Line Search
11 4/09 Constrained Optimization Problems (Chap 6, sec 7)
  • Equality constraints, inequality constraints
  • First Order conditions for optimality: KKT conditions
  • Penalty & barrier methods. (maybe dual ascent methods?)
  • Linear Programs.
  • HW4 due Apr 09.
11 4/11 MIDTERM II (on Thursday, in class).
12 4/16 Numerical Integration and Quadrature (Chap 8, secs 1-4,7)
  • Existence and Uniqueness
  • Numerical Quadrature (equally-spaced points).
  • Adaptive Quadrature
  • Richardson Extrapolation: Romberg.
13 4/23 Initial Val. Probs. for Ord. Diff. Equs
  • Existence and Uniqueness, stability of solutions
  • Linear ODEs
  • Methods: Euler, Backward Euler.
14 4/30 ... ODEs continued
  • Accuracy and Stability: local vs global truncation error
  • Runge-Kutta Methods
  • HW5 due May 02.
15 5/09 FINAL (on Thursday, 4-6pm).
Date Confirmed

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