University of Minnesota
CSci 5302 - Analysis of Numerical Algorithms
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CSCi 5302 - Spring 2022 -- Course Schedule

Last Revised 03/29/22 (provisional schedule, dates subject to change)

Textbooks

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WEEK DATE TOPICS
1 1/19 Scientific Computing - Goals and Fundamentals (H: Chap 1. A&G: 1.1-1.2, 2.1-2.3)
  • floating point arithmetic
  • relative error
  • conditioning vs stability: backward error vs forward error
  • truncation error vs rounding error.
2 1/24 Scalar Nonlinear Equs (H: 5.1 (5.2), 5.4. A&G: 3.1-3.4 )
  • Existence and Uniqueness
  • Sensitivity and Conditioning. backward error vs forward error
  • Methods: Bisection, Newton, Secant.
  • HW1 due Wed Jan 26
3 1/31 ... Nonlinear equations continued
  • General Fixed Point Methods.
  • Convergence Rates and Stopping Criteria
... ... Systems of Linear Equations (H: 2.1-2.4.7. A&G: Chap 9, 9.1)
  • Existence and Uniqueness
  • Norms.
4 2/07 ... Linear equations continued
  • Sensitivity and Conditioning.
  • Methods: Gaussian Elimination and Back Substitution.
5 2/14 Nonlinear Equations -- Systems (H: 5.4-5.6, [A&G: Chap 9])
  • HW2 due Mon Feb 14.
  • Partial Derivatives: gradients, Jacobians.
  • Fixed Point Methods. Newton's method.
6 2/21 Polynomial Interpolation (H: 7.1-7.3. A&G: 7.1-7.3)
  • Existence and Uniqueness
  • Methods: undetermined coefs.
6 2/22 Enhanced Homework I (out Monday, due Tuesday).
7 2/28 ... Interpolation continued
  • Methods: Lagrange polynomials. divided differences.
... ... Splines (H: 7.4. A&G: 11.3, 11.6)
  • Piecewise polynomial interpolation: splines.
  • Two-dimensional interpolation/splines (from notes).
=== 3/07 SPRING BREAK
  • Romp in the virtual sand.
8 3/14 Linear Least Squares (H: 3.1-3.2. A&G: 6.1)
  • HW3 due Fri Mar 04.
  • Existence and Uniqueness
  • Normal equations.
9 3/21 Unconstrained Optimization Problems (H: 6.1-6.5. A&G: Chap 9, 3.5,9.2-9.3)
  • First & second order conditions for optimality in 1D, gradients, Hessians.
  • One-dimension: Golden Section Search.
  • Existence and Uniqueness: coercive and convex functions
  • Conditioning
10 3/28 Unconstrained Optimization Problems (continued)
  • Conditioning
  • First & second order conditions for optimality (multi-dim): gradients, Hessians.
  • Multi-dimensional methods: steepest descent, Newton, BFGS.
  • Line Search
11 4/04 Constrained Optimization Problems (H: 6.7. A&G: 9.3)
  • HW4 due Mon Apr 04.
  • Conditioning
  • First & second order conditions for optimality (multi-dim): gradients, Hessians.
  • Equality constraints, inequality constraints
  • First Order conditions for optimality: KKT conditions
12 4/11 Enhanced Homework II (out Monday, due Tuesday).
12 4/11 Constrained Optimization Problems (continued)
  • Penalty & barrier methods. (maybe dual ascent methods?)
  • Linear Programs.
13 4/18 Numerical Integration and Quadrature (H: 8.1-8.4, 8.7. A&G: 15.1-15.2,15.4-15.5)
  • HW5 due Mon Apr 18
  • Existence and Uniqueness
  • Numerical Quadrature (equally-spaced points).
  • Adaptive Quadrature
  • Richardson Extrapolation: Romberg.
14 4/25 Initial Val. Probs. for Ord. Diff. Equs (H: 9.1-9.3. A&G: 16.1-16.6.)
  • Existence and Uniqueness, stability of solutions
  • Linear ODEs
  • Methods: Euler, Backward Euler.
  • Runge-Kutta Methods
  • Accuracy and Stability: local vs global truncation error
15 5/02 review
  • HW6 due Mon May 02.
Final 5/09 Enhanced Homework III (out Monday, due Tuesday).

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