A short table gives at

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics

Mathematical Methods for Physics, Ch Root finding, interpolation, numerical linear algebra and quadrature

Problem

A short table gives

\ln x

x = 1

2

and

4

only:

0

0.693147

and

1.386294

. ((a)) Write the quadratic interpolant

g_2

through these three points in Lagrange's form and evaluate

g_2(3)

. ((b)) Bound

|\ln 3 - g_2(3)|

with the interpolation error, using

f'''(x) = 2/x^3

. ((c)) Compare the bound with the actual error, using

\ln 3 = 1.098612

. Find the

\xi

at which the error formula holds exactly, and say why the bound is so loose here.

Browse the problem library