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- In Matlab, what does polyfit do? What does polyval do?
polyfit computes the coefficients of a polynomial that approximates a data set; polyval evaluates a polynomial (but the polynomial need not come from
polyfit)
- Suppose that you are given a data value C and wish to calculate an answer f(C). Let C = 3,000 and suppose that C is accurate to 4 significant digits. If the scaling factor for this calculation is 100, what is
your prediction for the relative error in f(C)?
(rel. error in f(C)) = (scaling factor)*(rel. error in C)
= 100*.0001 = .01
- To approximate the value of a derivative f’(x) we used the formula f’(x) = [ f(x+e) - f(x) ] / e where e is some “small” number. What motivates us to choose e as small as possible?
the small the value of
e, the more accurately the formula approximates the derivative (in the mathematical sense)
- What motivates us not to choose e as small as possible?
when we calculate this on the computer, and when e is very small, there is cancellation in the calculation, and if e is too small, the
computational error will be large
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