Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

374 Approximate Calculations (Ch 10
Solution. Taking y
We can thus take
= 4.457, we have
0.543
~ 5 =0.538;
1.009 ^i.oog
a,_5-4.457
0.565-0.435 0.220
2 1.009
= 0.538 + 0.027 = 0.565;
:0, 538 + 0. 027 = 0. 565.
* = 2. 2 + 0. 565- 0.2 = 2. 2 + 0. 113 = 2. 313.
2. Lagrange's interpolation formula. In the general case, a polynomial of
degree n, which for *=*/ takes on given values yf (/ = 0, 1, .... n), is given
by the Lagrange interpolation formula
__ (x *!> (x x 2) . . . (x x n ) (x XQ) (x * 2) . . . (x x n)
'
*o) (* *,). . .(X X k ^) (X
' "
' ' ' ^
3128. Given a table of the values of x and y:
Set up a table of the finite differences of the function y.
3129. Set lip a table of differences of the function y = x*
5jc f + JC 1 for the values *=1, 3, 5, 7, 9, 11. Make sure that
all the finite differences of order 3 are equal.
3130*. Utilizing the constancy of fourth-order differences, set
up a table of differences of the function y = x* 10*' +2** + 3jt
for integral values of x lying in the range l^jt^lO.
3131. Given the table
log 1=0.000,
log 2 -0.301,
log 3 = 0.477,
log 4 = 0.602,
log 5 = 0.699.
Use linear interpolation to compute the numbers: log 1.7, Iog2.5,
log 3.1, and log 4. 6.