Date | Topics | Materials |
---|---|---|
Jan 23 | Overview, Julia |
Notes Julia: A Fresh Approach to Numerical Computing |
Jan 25 | IEEE floating-point arithmetic |
Notes macheps.jl Driscoll & Braun, Floating-point numbers Overton, 2001 |
Jan 30 | Bisection, secant, and Newton's method |
Suli & Mayers: 1.4 - 1.6 Notes |
Feb 1 |
Convergence of Newton's method, rates of convergence, nonlinear systems |
Suli & Mayers: 1.4, 1.7 Notes |
Feb 6 | Vector and matrix norms, conditioning |
Suli & Mayers: 2.7 Driscoll & Braun: 2.7 Driscoll & Braun: 2.8 Notes |
Feb 9 | Multivariate Newton |
Driscoll & Braun: 4.5 Notes |
Feb 13 | Optimization |
Driscoll & Braun: 4.6 Notes |
Feb 15 |
Gaussian elimination, LU Operation counts |
Driscoll & Braun: 2.2 Driscoll & Braun: 2.3 Driscoll & Braun: 2.4 Driscoll & Braun: 2.5 Trefethen & Bau: Lectures 20-23 Notes |
Feb 20 | NO CLASS, PRESIDENTS' DAY | |
Feb 22 |
Cholesky, pivoted LU, Backward stability, Gram-Schmidt |
Driscoll & Braun: 2.6 Driscoll & Braun: 2.8 Driscoll & Braun: 2.9 Driscoll & Braun: 3.3 Trefethen & Bau: Lectures 20-23, 7-8 Notes |
Feb 27 |
Modified Gram-Schmidt, Householder reflections |
Trefethen & Bau: Lectures
6-11 Notes |
Mar 1 |
Householder reflections, linear regression, singular value decomposition |
Trefethen & Bau: Lectures
10-11,4-5 Notes |
Mar 6 | Power method, with shift |
Suli & Mayers: 5.4, 5.8 Notes |
Mar 8 | MIDTERM | |
Mar 13 | NO CLASS - SPRING BREAK | |
Mar 15 | NO CLASS - SPRING BREAK | |
Mar 20 |
Inverse power method with shift, Jacobi's method |
Suli & Mayers: 5.8, 5.3 Trefethen & Bau: Lectures 27, 30 Notes |
Mar 22 |
Convergence of Jacobi's method, QR algorithm |
Suli & Mayers: 5.3, 5.5-5.7.2 QR Algorithm Trefethen & Bau: Lectures 28-29 Notes |
Mar 27 |
Numerically computing the SVD Lagrange interpolation |
Trefethen & Bau: Lectures 4, 31 Suli & Mayers: 6.1-6.2 Notes |
Mar 29 |
Barycentric Lagrange interpolation, minimax approximation |
Suli & Mayers: 6.1-6.3, 8 Notes 1 Notes 2 |
Apr 3 | Chebyshev interpolation, 2-norm approximation |
Suli & Mayers: Ch 8-9 Notes 1 Notes 2 |
Apr 5 |
Orthogonal polynomials, trapezoidal rule |
Suli & Mayers: Ch 9 Notes 1 Notes 2 |
Apr 10 |
Composite trapezoidal rule, Euler-MacLaurin, Clenshaw-Curtis quadrature |
Suli & Mayers: Ch 7 Notes |
Apr 12 | Richardson extrapolation, Gaussian-Quadrature |
Suli & Mayers: Ch 7.7, 10 Notes |
Apr 17 |
Intro to Fourier series Discrete Fourier analysis |
Briggs & Henson: Ch 1, 2.1-2.5 |
Apr 19 | NO CLASS | |
Apr 24 | Fast Fourier Transform | Briggs & Henson: Ch 10 |
Apr 26 |
Spectral differentiation and integration, Clenshaw-Curtis quadrature (revisited) |
FFT differentiation Clenshaw-Curtis |
May 1 | Digital signal processing, convolutions | Briggs & Henson: Ch 7.2 |
May 3 | Iterative methods for linear systems: GMRES | Trefethen & Bau: Lectures 32-35 |
May 8 |
Iterative methods for linear systems: GMRES Review of course |
Trefethen & Bau: Lectures 32-35 |
May 11 | Final Exam 2:00pm - 3:50pm | CIWW, Room 201 |