Looking for TVM contributions

[Albert Chan]

(06-15-2024 09:52 PM)robve Wrote:  Newton takes 103 evaluations total over all tests, Secant takes 151 evaluations (though they are a bit cheaper), Hybrid takes 104 evaluations and these are cheaper than Newton.

From your C code, I am guessing this is done with IEEE double?
What is g? Why is it needed?

With lua tvm(), it finished it all with 132+12 = 144 evaluations (last 3 was duplicated tests)

24 test samples, f evaluations + final rate included (mode BEGIN → END, for first 3 cases)

Code:

rate_test = {
{40,i,900-40,-40,-1000+40       ,4, 0.04753367188571021},
{40,i,900+1000,1000,-1000-1000  ,2, -0.49999999999997724},
{40,i,900-400,-400,-1000+400    ,3, 0.8000000000098451},    -- x2
{31536000,i,0,-.01,3331667.0067 ,8, 1.1694311188017701e-07},
{525600,i,0,-.01,5282.367769    ,6, 1.902587523612461e-08},
{525600,i,0,-.01,5260.382426    ,6, 3.170979198140072e-09}, -- x2

{32,i,1-1e6,0,1e6               ,3, 3.125001611329216e-08}, -- x2
{360,i,0,-1e3,1e6               ,7, 0.004980365840090327},
{328,i,35e3,-324,0              ,5, 0.008720569148340681},
{58,i,-775,-49.56,4e3           ,6, 0.0026058787514755544},
{32,i,-6e3,0,1e4                ,6, 0.016091394922276913},
{48,i,19198,-450,0              ,6, 0.004918000645880568},

{5,i,-369494,17500,540000       ,6, 0.1200000561803591},
{348,i,243400,-1363.29,0        ,5, 0.00437501742139102},
{30,i,-3200,-717.44,60000       ,6, 0.048750016694561145},
{60,i,243400,-1363.29,-222975.98,4, 0.00437499988799056},
{24,i,0,-50.26,1281.34          ,7, 0.005209314607602606},
{6,i,-32000,0,28346.96          ,4, -0.019999978033474884},

{60,i,8000,-150.97,0            ,7, 0.004166696417110639},
{456,i,270000,-1215.333333,0    ,6, 0.0036443486419549583},
{480,i,100000,-208.333333,0     ,6, -6.652806639543341e-12},
{10,i,50,-30,400                ,7, 0.1443587132807996},
{10,i,50,-30,80                 ,5, -0.36893369874177734},
{10,i,-100,10,0                 ,7, 0},
}

Update: tested again, but with i=false instead of i=nil, to use big sized edge.
Again, it finished in 132+12 = 144 evaluations (last 3 was duplicated tests)

Basically the same solved rate, except for #22 and #23, with 2 sign changes. (0 or 2 roots)

Code:

#22 n=10 pv=50 pmt=-30 fv=400
small edge = -30/400 = -0.075 --> i =  0.1443587132807996
  big edge = -30/-50 =  0.60  --> i =  0.5317221326838473

#23 n=10 pv=50 pmt=-30 fv=80
small edge = -30/80 = -0.375  --> i = -0.36893369874177734
  big edge = -30/-50 =  0.60  --> i =  0.5846195526622099