Browsing by Subject "numerical analysis"

Now showing 1 - 3 of 3
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    Lectures on moving frames
    (2009-01-21) Olver, Peter J.
    This article surveys the equivariant method of moving frames, along with a variety of applications to geometry, differential equations, computer vision, numerical analysis, the calculus of variations, and invariant curve flows.
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    Numerical analysis of prediction with expert advice
    (2022-05) Mosaphir, Drisana
    This work investigates the online machine learning problem of prediction with expert advice through numerical analysis of a related PDE. The problem is a repeated two-person game involving decision-making at each step informed by n experts with geometric stopping condition; the continuum limit of the consequences of this game over a large number of steps leads to an elliptic PDE. This work presents a numerical scheme that allows us to solve this PDE for general number of experts n, and gives numerical results for n < 9.
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    Numerical Routing of Flood Hydrographs through Open Channel Junctions
    (Water Resources Research Center, University of Minnesota, 1971-08) Bowers, C. Edward; Larson, Curtis L.; Wei, Tsong C.
    The study was concerned with numerical routing of flood hydrographs through open channel junctions. An open channel junction with a main channel above and below plus a branch channel were constructed in the laboratory. All channels were rectangular in shape, but varied in size. Facilities and procedures for supplying hvdrographs to the two channels above the junction were developed. Provision was made for measuring both inflow and outflow hydrographs and also flow depths at selected points in the three channels. A total of 14 experiments were conducted with various combinations of input hydrographs in terms of magnitude and relative timing. Unsteady flow conditions (depth, velocity and discharge) in the three channels were calculated at calculated at 5-ft. length increments and 1-sec. time increments, using the method of explicit finite differences applied to the characteristic equations. A procedure for calculating unsteady flow backwater effects in either or both of the upstream channels was developed and utilized as an integral part of the routing method. The junction routing procedure appears to be fairly general, having been applied in a situation where the channels above and below the junction are at different size, slope and elevation. In particular, it was shown that unsteady flow backwater effects can be represented in the method of explicit finite differences applied to the characteristic equations. Some error can be expected in any numerical method, as well as in all measurements. Due to the measurement error cited above, the amount of error attributable to the routing method cannot be determined. It appears to be on the order of 6 percent, but could be less than this amount.