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golden section search - similar to bisection method, use an interval that contains point of interest
successive parabolic interpolation- use parabolas that keep trying to approximate what the function looks like at the minimum point
- review 1 norm (minimize all error, least sensitive to outliers), 2 norm (minimize area of boxes of error), infinity norm errors (minimize largest error, most sensitive to outliers)
-fminsearch (function, initialguess) = only accepts a vector
x = fminsearch(fun,x0)
fminsearch(@(x) -func(x),1)
-fminbnd(function, lower bound, upperbound ) = only accepts
x = fminbnd(fun,x1,x2)
-find max: fminbnd(-function,lb,up)
fminbnd(@(x) -func(x),1,3)
polyfit - fits a polynomial to the data in a least squared error sense (by minimizing the 2-norm of the data)
returns three values: 1st value: x^2 coefficient 2nd value: x coefficient 3rd value: constant
pfit=polyfit(X,Y,2)
the third parameter is the highest degree polynomial you would like (2 means the highest power is x^2 so 2nd degree polynomial)
in order to ensure it will go through all of the points, choose a third parameter that is N-1 (number of data points -1) -- this wouldn't be very useful though, because it wouldn't really tell us anything (doesn't really follow a general trend); weak explanatory power, good for interpolation
number of unknowns in the polynomial= highest power+1
plot(xvalues, polyval(pfit, xvalues) ) -- polyval will help plot the polynomial from the polyfit command that spits out the coefficients alone
interpolation- is useful when data is smooth, or spread out (not too many data points). also when you want to generate new data and treat your current data as "true"
interp1(X,Y,xvalues)
third parameter is what points exactly I want them to go through (it must connect those dots so they can find values in between)
X and Y are just the domain and range
- review gradient descent
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