Looking for TVM contributions

[Albert Chan]

(06-20-2024 04:30 PM)robve Wrote:  Well, try this example with Newton. The curve is parabolic with f''>0. We stop at sign change and take the last i%:
./tvm 10 '?' 50 -12.8277219567 80
...
10, i%=4.07241726070281285%, FVerr=2e-10

This is not a winning strategy IMHO. Newton stopping at non-monotonicity is better with previous i% when the last step wasn't monotonically decreasing:

12, i%=4.07241726070545784%, FVerr=2.8e-14

With the Hybrid method we have no sign change and we hit the root even closer:

14, i%=4.07241726070100896%, FVerr=1.4e-14

Solve with mpmath, mp.dps = 34, rounded back to float
rate1(%) = 4.14000005643961 -- ignored for error analysis
rate2(%) = 4.0724172607043148

Newton error =  1.502e-12 %
Secant error = -1.143e-12 %
Hybrid error =  3.306e-12 %