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Outline and Notes

Complete lecture notes (in one pdf)

Notes for each lecture are made available in advance subject to the disclaimer that they may not precisely match the lecture itself. Please let me know if you spot any typos.

Lectures Notes
Mon 12th Jan Introduction and (0) Revision of polynomial interpolation
Thu 15th Jan (0.1) Chebyshev interpolation
Mon 19th Jan (1) Piecewise polynomial interpolation, (1.1) Linear splines
Thu 22nd Jan (1.2) Cubic splines [updated]
Mon 26th Jan (1.2) Cubic splines continued [updated]
Thu 29th Jan (1.3) B-splines
Mon 2nd Feb (2) Minimax approximation, (2.1) Weierstrass approximation theorem
Thu 5th Feb (2.2) Bezier curves
Mon 9th Feb (2.3) Minimax approximations
Thu 12th Feb (2.4) Alternating sets
Mon 16th Feb (2.5) Chebyshev Equioscillation Theorem
Thu 19th Feb (2.6) Remez/Exchange Algorithm
Mon 23rd Feb (3) Trigonometric interpolation (3.1) The discrete Fourier transform
Thu 26th Feb (3.1) The discrete Fourier transform continued and (3.2) Aliasing [updated]
Mon 2nd Mar (3.3) The Fast Fourier Transform
Thu 5th Mar (3.4) The Discrete Cosine Transform
Mon 9th Mar (3.5) Image Compression
Thu 12th Mar (3.5) Image Compression continued

Interesting Links

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The error curves $f(x)-p(x)$ for two different polynomial approximations of degree 100 to the function $f(x)=|x-\frac{1}{4}|$. The first is the ``minimax'' polynomial approximation (red) and the second is the interpolant at the Chebyshev nodes (blue).