14:00
First, I'll give a very brief update on our nonlinear Krylov accelerator for the usual Modified Newton's method. This simple accelerator, which I devised and Neil Carlson implemented as a simple two page Fortran add-on to our implicit stiff ODEs solver, has been robust, simple, cheap, and automatic on all our moving node computations since 1990. I publicize further experience with it here, by us and by others in diverse fields, because it is proving to be of great general usefulness, especially for solving nonlinear evolutionary PDEs or a smooth succession of steady states.
Second, I'll report on some recent work in computerized tomography from X-rays. With colored computer graphics I'll explain how the standard "filtered backprojection" method works for the classical 2D parallel beam problem. Then with that backprojection kernel function H(t) we'll use an integral "change of variables" approach for the 2D fan-beam geometry. Finally, we turn to the tomographic reconstruction of a 3D object f(x,y,z) from a wrapped around cylindical 2D array of detectors opposite a 2D array of sources, such as occurs in PET (positron-emission tomography) or in very-wide-cone-beam tomography with a finely spaced source spiral.