Abstract:
Anyone who uses Matlab will enjoy Chebfun, a freely-available package that overloads Matlab's familiar operations on vectors to apply to functions of a continuous variable. Thus in Matlab, SUM(f) adds up the entries of a vector, but in Chebfun, it computes the integral of a function. MAX(f) finds the maximum, ROOTS(f) finds the roots, and so on. Under the hood, everything is based on piecewise expansions in Chebyshev polynomials, but in principle you don't need to know that.
This talk will be a hands-on demonstration, and attendees are welcome to bring a laptop running Matlab if they want try Chebfun on the spot. Just as Chebfun turns vectors into functions, it turns matrices into operators, notably differential and integral operators. One of our proudest achievements is that we've overloaded Matlab's backslash command to solve linear and nonlinear differential equations, typically to close to machine precision in a fraction of a second.
