Alan Edelman showed that for a perturbation of Gould’s matrix

a growth factor of 13.02 is achieved

in exact arithmetic.

He also found matrix of size 25 for which the growth factor is

32.986341.

Alan Edelman, The Complete Pivoting Conjecture for Gaussian Elimination is

False, The Mathematica Journal 2, 58-61, 1992.

2) You can’t make a change of variable that alters the time scale of just part of the problem. Unless you have decoupled problems. ]]>

1) It seems that you numerical people like so much the analogy with the hike along a narrow and long canyon that you also use it to explain why the steepest descent is also a slow method compared to conjugate gradient. Is the similarity only a coincidence or is there something common to the two problems, stiffness and minimization?

2) In the section “Stiffness in Action” you make the remark ” You don’t want to change the differential equation”. If the problem of stiffness boils down to having a differential equation with two or more very different time scale, could one make use of a transformation that contracts the times?

]]>Thanks for posting this..looking forward to hearing about subnormal/denormal numbers in your next post.

]]>Looking forward to the second part! This is very interesting subject. I’ve hit some of the floating point numbers limitations when studying relativity theory (with the help of MATLAB).

Could you please elaborate more on “t1 < 1/10 < t2"? It seems that t1 is the same formula as t2 in your equations.

Thank you!

]]>— Cleve ]]>