A finite-difference model of heat flow in a rod gives a linear system whose matrix has
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics
Error, Chance and the Machine, Ch Rounding, backward error and the sensitivity of a computation
Problem
A finite-difference model of heat flow in a rod gives a linear system whose matrix has κ2(A)=2.5×105. The system is solved by a backward stable method.
((a)) Estimate κ2u and the number of correct significant digits to expect in binary64 (t=53).
((b)) Do the same in binary32 (t=24).
((c)) Do the same in half precision (t=11), and say what the answer means.