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| Lecture Notes: |
A PDF of the course notes is provided here, with additional links/demos to be posted below.
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| Lecture 38 (11/21): |
NSODE: stiff systems of ODEs
Lecture 32 in the course lecture notes.
Notes from class
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| Lecture 37: |
NSODE: linear multistep methods, absolute stability
Lecture 31 in the course lecture notes.
Notes from class
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| Lecture 36: |
NSODE: linear multistep methods and zero stability
Lecture 31 in the course lecture notes.
Notes from class
Julia demo
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| Lecture 35: |
NSODE: linear multistep methods, accuracy
Lecture 30,31 in the course lecture notes.
Notes from class
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| Lecture 34: |
NSODE: linear multistep methods
Lecture 30 in the course lecture notes.
Notes from class
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| Lecture 33: |
NSODE: truncation and global error
Lecture 29 in the course lecture notes.
Lecture 12.3 in Suli and Mayers.
Onestep error demo
Notes from class
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| Lecture 32: |
Intro to numerical solution of ODEs (NSODE)
Lecture 28-29 in the course lecture notes.
Lecture 12.1-12.2 in Suli and Mayers.
Notes from class
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| Lecture 31: |
Eigenvalue computations: practical QR algorithm
Lecture 37 in the course lecture notes.
Lecture 27,28 in Trefethen and Bau.
Demo of QR algorithm
Notes from class
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| Lecture 30: |
Eigenvalue computations: QR algorithm
Lecture 37 in the course lecture notes.
Notes from class
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| Lecture 29: |
Eigenvalue computations: power, inverse, and Rayleigh quotient iteration
Lecture 37 in the course lecture notes.
Notes from class
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| Lecture 28: |
Cholesky factorization
Lecture 36 in the course lecture notes.
Notes from class
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| Lecture 27: |
LU decomposition with partial pivoting
Lecture 35,36 in the course lecture notes.
Notes from class
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| Lecture 26: |
Singular value decomposition: low rank approximation
Lecture 18 in the course lecture notes.
Notes from class
Reference for SVD analysis of Congressional voting patterns
Congressional SVD analysis demo
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| Lecture 25: |
SVD and matrix norms, condition numbers, and subspaces
Lecture 17,18 in the course lecture notes.
Notes from class
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| Lecture 24: |
Singular value decomposition
Lecture 17,18 in the course lecture notes.
Notes from class
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| Lecture 23: |
QR decomposition via modified Gram-Schmidt.
Lecture 3-4 in the course lecture notes.
Notes from class
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| Lecture 22: |
Householder reflectors, QR decomposition
Lecture 3-4 in the course lecture notes.
Notes from class
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| Lecture 21: |
Linear algebra: norms, projectors, reflectors
Lecture 2 in the course lecture notes.
Notes from class
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| Lecture 20: |
Gaussian quadratures: error bounds
Lecture 25 in the course lecture notes.
Suli and Mayers 10.2
Notes from class
gauss_quad_demo.jl: Gauss quadrature demo compared with trapezoidal rule on [-1,1].
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| Lecture 19: |
Gaussian quadratures
Lecture 25 in the course lecture notes.
Suli and Mayers 10.
Notes from class
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| Lecture 18: |
Richardson extrapolation and Romberg integration.
Lecture 24 in the course lecture notes.
Notes from class
Suli and Mayers 7.7.
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| Lecture 17: |
Quadrature: error bounds, composite rules.
Lecture 23 in the course lecture notes.
Notes from class
Suli and Mayers 7.1-7.5.
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| Lecture 16: |
Continuous L2 approximation, orthogonal polynomials.
Lecture 19,20 in the course lecture notes.
Suli and Mayers 9.4.
Notes from class
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| Lecture 15: |
Continuous least squares approximation.
Lecture 19,20 in the course lecture notes.
Notes from class
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| Lecture 14: |
B-spline bases.
Lecture 13,14 in the course lecture notes.
Notes from class
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| Lecture 13: |
Spline interpolation.
Lecture 13,14 in the course lecture notes.
Notes from class
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| Lecture 12: |
Optimal interpolation points from minimax theory, quadrature.
Lecture 22,23 in the course lecture notes.
Notes from class
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| Lecture 11: |
Minimax approximations.
Correction to class notes: the minimax linear approximation to e^x has points at the end due to convexity, not monotonicity.
Lecture 21 in the course lecture notes.
Additional reading: Suli and Mayers 8.3
Notes from class
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| Lecture 10: |
Hermite interpolation error analysis, piecewise polynomial interpolation.
Lecture 13,14 in the course lecture notes.
hermite_interp.jl showing Hermite interpolation of function and derivative values at equispaced points.
p1_interp_demo.jl showing a comparison between piecewise linear and high order polynomial interpolation.
Notes from class
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| Lecture 9: |
Newton divided differences, Hermite interpolation.
Lecture 13,14 in the course lecture notes.
Additional reading: Suli and Mayers 11.
Notes from class
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| Lecture 8: |
Polynomial interpolation: problems with monomials. Lagrange and Newton bases.
Lecture 10,11 in the course lecture notes.
Additional reading: Suli and Mayers 6.3.
Notes from class
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| Lecture 7: |
Polynomial interpolation: error analysis
Lecture 9, 10 in the course lecture notes.
Additional reading: Suli and Mayers 6.1-6.3.
Demo showing convergence of interpolation along with an error bound.
Notes from class
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| Lecture 6: |
Fixed point error analysis, polynomial interpolation.
Lecture 9, 10 in the course lecture notes.
Additional reading: Suli and Mayers 6.1-6.3.
Demo of interpolation using Vandermonde matrix.
Notes from class on fixed point
Notes from class on polynomial interpolation
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| Lecture 5: |
Rate of convergence for secant method, fixed point iterations.
Lecture 40 in the course lecture notes.
Additional reading: Suli and Mayers 1.1-1.3.
Notes from class
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| Lecture 4: |
Root finding: secant method and its convergence.
Lecture 40 in the course lecture notes.
Additional reading: Suli and Mayers 1.1-1.3.
Notes from class
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| Lecture 3: |
Root finding: convergence of Newton's method.
Lecture 39 in the course lecture notes.
Thm 1.9 in Suli/Mayers
Notes from class
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| Lecture 2: |
Root finding: bisection and Newton's method.
Lectures 38,39 in the course lecture notes.
Additional reading: Suli and Mayers 1.4, 1.6.
Julia rootfinding demo
Notes from class
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| Lecture 1: |
Introduction to Numerical Analysis:
Floating point number systems, catastrophic cancellation.
Rounding error disasters
Lectures 1,8 in the course lecture notes.
Notes from class
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