notesonCompScipaper.nb

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Substitution of the above equation into our first equation, yields\
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To implement the above equation, we need to first transform our source \
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Next, we compute our low rank f(x) at each observation point with our \
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Now we can approximate the kernel with the above interpolation formula. First \
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                    True, FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
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                    AbsoluteCurrentValue[Magnification]}]], 
                    "RGBColor[1, 0, 0]"], Appearance -> None, BaseStyle -> {},
                     BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
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                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
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               RowBox[{
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                 TagBox[#2, HoldForm], ",", 
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             RowBox[{"LabelStyle", "\[Rule]", 
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      GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
      AutoDelete -> False, GridBoxItemSize -> Automatic, 
      BaselinePosition -> {1, 1}]& ),
    Editable->True,
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       RowBox[{#, ",", 
         RowBox[{"Placed", "[", 
           RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )], ",", 
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Very much near exact for n - 1 > leading order of polynomial. Error does in \
fact grow with the larger orders as stated in this work. Turns out, the \
convergence properties of these functions are very good.  See the paper for \
more details. Anyway, now that it is clear that the interpolation scheme is \
useful, we can write a interpolation scheme for our low-rank kernel. We\
\[CloseCurlyQuote]ll stick to 1D for now\
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Cell["Low-rank kernel, Chebyshev interpolation", "Section",
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