kl_2012_fsu

kl_2012_fsu, "Covariance, Correlation, and the KL-Expansion", a discussion of the Karhunen-Loeve expansion, written in 2012 at Florida State University.

• kl_2012_fsu.tex
• kl_2012_fsu.pdf

The following files were used:

• airline_passengers.png, a plot of airline passenger traffic.
• beta_pdf.png, a plot of the Beta probability density function.
• beta_sample.png, a plot of a histogram of Beta samples.
• brown_paper.png, the first page of Robert Brown's report on Brownian motion.
• brownian_correlation.png, a plot of the Brownian correlation function.
• brownian_motion_1d.png, a plot of 1D Brownian motion.
• brownian_motion_2d.png, a plot of 2D Brownian motion.
• clayton_test01.m, a MATLAB program which plots correlation functions for two values of the correlation length.
• clayton_besselj_plots.png,
• clayton_besselk_plots.png,
• clayton_circular_plots.png,
• clayton_constant_plots.png,
• clayton_cubic_plots.png,
• clayton_damped_cosine_plots.png,
• clayton_damped_sine_plots.png,
• clayton_exponential_plots.png,
• clayton_gaussian_plots.png,
• clayton_linear_plots.png,
• clayton_pentaspherical_plots.png,
• clayton_rational_quadratic_plots.png,
• clayton_spherical_plots.png,
• clayton_white_noise_plots.png,
• clayton_chebfun_test01.m, a MATLAB program which computes and displays 5 eigenfunctions for the gaussian correlation, with correlation length 1/4 and 1.
• clayton_chebfun_gaussian_0.25.png,
• clayton_chebfun_gaussian_1.0.png,
• clayton_chebfun_test02.m, a MATLAB program which computes and displays 5 eigenfunctions for the exponential correlation, with correlation length 1/4 and 1.
• clayton_chebfun_exponential_0.25.png,
• clayton_chebfun_exponential_1.0.png,
• clayton_chebfun_allfour.png, all four of the immediately previous plots, concatenated using imagemagick: "convert a.png b.png +append ab.png", "convert c.png d.png +append cd.png", "convert ab.png cd.png -append abcd.png".
• correlation_besselj_plot.png, a plot of the Bessel J correlation function.
• correlation_besselk_paths.png, a plot of realizations based on the Bessel K correlation function.
• correlation_besselk_plot.png, a plot of the Bessel K correlation function.
• correlation_damped_cosine_paths.png, a plot of realizations based on the damped cosine correlation function.
• correlation_damped_cosine_plot.png, a plot of the damped cosine correlation function.
• correlation_exponential_plot.png, a plot of the exponential correlation function.
• correlation_gaussian_paths.png, a plot of realizations based on the gaussian correlation function.
• correlation_gaussian_plot.png, a plot of the gaussian correlation function.
• fsu_sports_logo.pdf, a logo.
• ibm_stock.png, a plot of the value of IBM stock over time.
• mode_1.png, a plot of SVD U mode 1 (monthly variation, years averaged out).
• mode_2.png, a plot of SVD U mode 2 (monthly variation, years averaged out)..
• mode_3.png, a plot of SVD U mode 3 (monthly variation, years averaged out).
• mode_4.png, a plot of SVD U mode 4 (monthly variation, years averaged out).
• nile.png, a plot of yearly flood statistics for the Nile.
• paths.png, a plot ODE paths with varying initial condition.
• snow_1890_0.png, 1890 snowfall.
• snow_1890_1.png, rank 1 approximation to 1890 snowfall.
• snow_1890_2.png, rank 2 approximation to 1890 snowfall.
• snow_1890_3.png, rank 3 approximation to 1890 snowfall.
• snow_1890_4.png, rank 4 approximation to 1890 snowfall.
• snow_1890_5.png, rank 5 approximation to 1890 snowfall.
• snowfall.txt, monthly snowfall records.
• snowfall_1890.png, 1890 snowfall.
• snowfall_2008.png, 2008 snowfall.
• snowfall_s.png, singular values of the snowfall matrix.
• snowfall_svd.m, a MATLAB program to analyze the snowfall data.
• v_mode_1.png, a plot of SVD V mode 1 (yearly variation, months averaged out).
• v_mode_2.png, a plot of SVD V mode 2 (yearly variation, months averaged out).
• v_mode_3.png, a plot of SVD V mode 3 (yearly variation, months averaged out).
• v_mode_4.png, a plot of SVD V mode 4 (yearly variation, months averaged out).