math 361s lecture notes dierentiation and richardson extrapolation jerey wong february 23 2020 topics covered dierentiation finite dierences error analysis eect of rounding error deriving formulas using taylor series and ...
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...Math s lecture notes dierentiation and richardson extrapolation jerey wong february topics covered finite dierences error analysis eect of rounding deriving formulas using taylor series lagrange interpolation asymptotic use in estimating two approximations wenowconsider the problem for derivative f x a function at point its values nite set nearby points simplest is forward dierence h dened which obvious from denition to determine we simply expand hf edited by holden lee this gives formula with term where lies between particular o not very good about as inaccurate can be while still valid get better more or arrange them optimally there are several approaches basic method aformula n will have form xckf akh k coecients c important why must linear combination typically derivation goes follows decide e g stencil approximation see figure terms around keeping many needed given expect control rst should then taken plus an note some cases one below choose ck so that remains other cancel possibl...