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Material Type: Notes; Professor: Detar; Class: Intro To Comput In Phys; Subject: Physics; University: University of Utah; Term: Fall 2004;
Typology: Study notes
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Physics 6720 { Neville Interp olation { Novemb er 13, 2004
When it is exp ensive or dicult to evaluate a function f (x) at an arbitrary
value of x, we might consider, instead, interp olating from a table of values.
Consider the exp onential integral,
Ei(x) = P
x
e
t
dt=t
tabulated b elow for small x.
x Ei(x)
This function diverges as log(x) at x = 0. To evaluate it requires doing
the integral, or summing a series, so it is somewhat exp ensive. Supp ose we
want the value of Ei(0:15). A very crude approximation cho oses either of the
two nearby values Ei(0:1) = 1 : 6228 or Ei(0:2) = 0 :8218. A common and
somewhat b etter approach makes a linear interp olation. Since 0.15 is midway
b etween 0.1 and 0.2 the linear interp olation just averages the two values, giving
1 Lagrange Interp olation
Let's generalize the linear interp olation by denoting the values in the table
by (x i ; y i ) for i = 0 ; : : : ; n. Then a linear function interp olating the rst two
values can b e written as
(x) = y 0
x x 1
x 0