CS450 Calendar

Note: Some calendar entries are clickable and link to entries below.
Office Hours Hao (Nov. 16, 2018, 9:30 a.m. - Nov. 16, 2018, 10:30 a.m.)

Office: Siebel Center 0207

Office Hours Raul (Nov. 16, 2018, 1 p.m. - Nov. 16, 2018, 2 p.m.)

Office: Siebel Center 0207

Office Hours Kaushik (Nov. 15, 2018, 10:30 a.m. - Nov. 15, 2018, 11:30 a.m.)

Office: Siebel Center 0207

Office Hours Kaushik (Nov. 15, 2018, 11:30 a.m. - Nov. 15, 2018, 12:30 p.m.)

Office: Siebel Center 0207

Office Hours Isuru (Nov. 15, 2018, 3:30 p.m. - Nov. 15, 2018, 4:30 p.m.)

Office: Siebel Center 0207

Office Hours Hao (Nov. 14, 2018, 9:30 a.m. - Nov. 14, 2018, 10:30 a.m.)

Office: Siebel Center 0207

Office Hours Raul (Nov. 14, 2018, 11 a.m. - Nov. 14, 2018, noon)

Office: Siebel Center 0207

Lecture 20 (Nov. 5, 2018, 3:30 p.m. - Nov. 5, 2018, 4:45 p.m.)

Lecture Notes

  • Introduction to interpolation
  • Vandermonde systems and conditioning
  • Polynomial bases
  • Chebyshev nodes

Quiz 18: Basics of Interpolation

Lecture 19 (Oct. 31, 2018, 3:30 p.m. - Oct. 31, 2018, 4:45 p.m.)

Lecture Notes

  • Nonlinear least squares and Gauss-Newton
  • Constrained optimization optimality
  • Sequential quadratic programming
  • Active set methods
  • Penalty and barrier methods

Quiz 17: Multidimensional Unconstrained Optimization Algorithms

Lecture 18 (Oct. 29, 2018, 3:30 p.m. - Oct. 29, 2018, 4:45 p.m.)

Lecture Notes

  • Golden section search
  • Steepest descent
  • Convergence of steepest descent and extrapolation methods
  • Conjugate gradient
  • Newton's method for multidimensional unconstrained optimization

Quiz 16: Multidimensional Unconstrained Optimization Algorithms

Lecture 17 (Oct. 24, 2018, 3:30 p.m. - Oct. 24, 2018, 4:45 p.m.)

Lecture Notes

  • Numerical optimization introduction
  • Conditions of optimal solutions
  • Golden section search
  • Newton's method and quasi-Newton methods for 1D problems
  • Safeguarding techniques
  • Steepest descent

Quiz 15: Optimization Problems and Algorithms for 1D Optimization

Lecture 16 (Oct. 22, 2018, 3:30 p.m. - Oct. 22, 2018, 4:45 p.m.)

Lecture Notes

  • Secant method
  • Convergence of fixed point iteration and Newton's method for multidimensional nonlinear solve
  • Broyden's method
  • Safeguarding techniques

Activity: Broyden's Method

Quiz 14: Cost and Robustness of Methods for Solving Nonlinear Equations

Examlet 2 (Oct. 18, 2018, 9 a.m. - Oct. 20, 2018, 10 p.m.)

As you may have seen in our class policies, our "examlets" and "finals" will take place in a computer-based testing facility ("CBTF") in Grainger Library.

You must schedule your test appointment with the Computer-Based Testing Facility at this link. This examlet is now available for scheduling.

Find out more about the testing facility, such as:

  • where it is
  • when to show up
  • what to bring (and not to bring)

The exam will be 50 minutes in length, and it will cover the material of the first four chapters.

Examlet 2 Study Guide

Examlet 1 Study Guide

Lecture 15 (Oct. 17, 2018, 3:30 p.m. - Oct. 17, 2018, 4:45 p.m.)

Lecture Notes

  • Introduction to nonlinear function solve problems
  • Existence, uniqueness, and conditioning of roots
  • Multiplicity of roots and conditioning
  • Convergence rates
  • Bisection algorithms
  • Fixed-point functions and convergence
  • Newton's method

Activity: Newton's Method for 2-by-2 System of Equations

Quiz 13: Basic Methods for Solving Nonlinear Equations

Lecture 14 (Oct. 15, 2018, 3:30 p.m. - Oct. 15, 2018, 4:45 p.m.)

Lecture Notes

  • Review orthogonal iteration and QR iteration
  • Divide and conquer for tridiagonal eigenproblem
  • Krylov subspace methods
  • Ritz values and vectors

Activity: Orthogonal Iteration

Quiz 12: Tridiagonal Eigenproblems and Krylov Subspace Methods

Lecture 13 (Oct. 10, 2018, 3:30 p.m. - Oct. 10, 2018, 4:45 p.m.)
Lecture 12 (Oct. 8, 2018, 3:30 p.m. - Oct. 8, 2018, 4:45 p.m.)

Lecture Notes

  • Similarity and matrix types
  • Canonical forms: Schur and Jordan forms
  • Obtaining eigenvalues from triangular matrices
  • Conditioning and sensitivity of eigenvalue decomposition and eigenpairs
  • Convergence of power iteration
  • Deflation

Quiz 10: Canonical Forms for Eigenvalue Problems and Deflation

Activity: Calculating Eigenpairs of Triangular Matrix

Lecture 11 (Oct. 3, 2018, 3:30 p.m. - Oct. 3, 2018, 4:45 p.m.)

Lecture Notes

  • Eigenvalues and similarity
  • Eigenvalue decomposition
  • Power iteration, inverse iteration, Rayleigh-Quotient iteration
  • Conditioning, Gershgorin theorem

Quiz 9: Conditioning and Basic Algorithms for Eigenvalue Problems

Activity: Rayleigh Quotient Iteration

Lecture 10 (Oct. 1, 2018, 3:30 p.m. - Oct. 1, 2018, 4:45 p.m.)
  • Review lecture for eigenvalue problems

Activity: Inverse Iteration with a Shift

Lecture 9 (Sept. 26, 2018, 3:30 p.m. - Sept. 26, 2018, 4:45 p.m.)

Lecture Notes

  • Householder QR
  • Givens QR
  • Rank-deficient least squares
  • Truncated SVD and Eckart-Young-Mirsky theorem
  • Tykhonov regularization
  • QR with column pivoting

Quiz 8: Least Squares Algorithms and Rank-Deficiency

Activity: Rank Deficient Least Squares Problems

Lecture 8 (Sept. 24, 2018, 3:30 p.m. - Sept. 24, 2018, 4:45 p.m.)
  • Review lecture for least squares

Activity: Householder QR

Examlet 1 (Sept. 20, 2018, 9 a.m. - Sept. 23, 2018, 10 p.m.)

As you may have seen in our class policies, our "examlets" and "finals" will take place in a computer-based testing facility ("CBTF") in Grainger Library.

You must schedule your test appointment with the Computer-Based Testing Facility at this link. This examlet is now available for scheduling.

Find out more about the testing facility, such as:

  • where it is
  • when to show up
  • what to bring (and not to bring)

The exam will be 50 minutes in length, and it will cover the material of the first two chapters.

Examlet 1 Study Guide

Lecture 7 (Sept. 19, 2018, 3:30 p.m. - Sept. 19, 2018, 4:45 p.m.)

Lecture Notes

  • Linear least squares motivation and introduction
  • Conditioning of linear least squares
  • QR factorization
  • Normal equations and Cholesky QR
  • Gram-Schmidt methods
  • Householder QR

Quiz 7: Least Squares and QR Factorization

Lecture 6 (Sept. 17, 2018, 3:30 p.m. - Sept. 17, 2018, 4:45 p.m.)

Lecture Notes

  • Pivoting in LU
  • Multiplier growth and stability
  • Cholesky and other specialized factorizations
  • Sherman-Morrison-Woodbury formula

Quiz 6: Stability and Matrix Structure in Solving Linear Systems

Activity: Sherman-Morrison-Woodbury Formula

Lecture 5 (Sept. 12, 2018, 3:30 p.m. - Sept. 12, 2018, 4:45 p.m.)

Lecture Notes

  • Solving triangular systems of equations
  • LU factorization existence
  • LU with partial pivoting
  • Error in LU factorization

Quiz 5: Gaussian Elimination

Lecture 4 (Sept. 10, 2018, 3:30 p.m. - Sept. 10, 2018, 4:45 p.m.)

Lecture Notes

  • Orthogonal matrices
  • Singular values and conditioning
  • Peturbation analysis of linear systems

Quiz 4: Matrix Conditioning and Error in Linear Systems

Activity: Singular Value Decomposition and Norms

Lecture 3 (Sept. 5, 2018, 3:30 p.m. - Sept. 5, 2018, 4:45 p.m.)

Lecture Notes

  • Error in floating point arithmetic
  • Vector and matrix norms
  • Matrix condition number

Quiz 3: Floating Point, Matrix Norms, and Matrix Condition Number

Lecture 2 (Aug. 29, 2018, 3:30 p.m. - Aug. 29, 2018, 4:45 p.m.)

Lecture Notes

  • Floating point representation
  • Floating point arithmetic
  • Roundoff error analysis

Quiz 2: Error, Conditioning, and Floating Point

Activity: Cancellation in Standard Deviation Computation"

Lecture 1 (Aug. 27, 2018, 3:30 p.m. - Aug. 27, 2018, 4:45 p.m.)

Lecture Notes

  • Course administration
  • Motivation
  • Applications
  • Error
  • Posedness
  • Conditioning

Quiz 1: Policies