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cosolver/FM/FMsamples/rootsFM.chk
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Case 1. Call FM_SECANT to find a root between 1 and 2
for f(x) = X**2 - 3.
Use KPRT = 0, so no output will be done in the routine, then
write the results from the main program.
A root for function 1 is 1.732050807568877293527446341506
Case 2. Find a root between 6 and 7 for f(x) = x*tan(x) - 1.
Use KPRT = 1, so FM_SECANT will print the result.
FM_SECANT. Function 2 11 iterations.
Estimated relative error = 7.767234M-58, Root:
6.4372981791719471203626398510256332453217341714480M+0
Case 3. Find a root between 1 and 5 for f(x) = gamma(x) - 10.
Use KPRT = 2, so FM_SECANT will print all iterations,
as well as the final result.
FM_SECANT. Begin trace of all iterations.
J = 0 f(AX) = -9.0000000000M+0 x:
1.0000000000000000000000000000000000000000000000000M+0
J = 0 f(BX) = 1.4000000000M+1 x:
5.0000000000000000000000000000000000000000000000000M+0
J = 1 f(x) = -8.6068421859M+0 x:
2.5652173913043478260869565217391304347826086956522M+0
J = 2 f(x) = -6.7051471157M+0 x:
3.4921840811950674768726054094643443433586793877230M+0
J = 3 f(x) = 4.5186929492M+2 x:
6.7605566635344553427953681683199185886633746295652M+0
J = 4 f(x) = -6.5259077772M+0 x:
3.5399733101293708712941683890968476230216022770789M+0
J = 5 f(x) = -6.3422248053M+0 x:
3.5858228954424667483373209259448565775174368926113M+0
J = 6 f(x) = 2.1049716711M+1 x:
5.1689221582444679282516848043680371219598475726118M+0
J = 7 f(x) = -4.3466346198M+0 x:
3.9523676110766884825207209243892885805725532099791M+0
J = 8 f(x) = -2.6325150260M+0 x:
4.1605832733470755491853842973219340298745655186153M+0
J = 9 f(x) = 1.3192340241M+0 x:
4.4803572620082733981333836380656569924036270263122M+0
J = 10 f(x) = -2.2137831189M-1 x:
4.3736053603780873000062328166200630474362567876779M+0
J = 11 f(x) = -1.5402542083M-2 x:
4.3889450764262963809325836229953951301411172475795M+0
J = 12 f(x) = 1.9744111815M-4 x:
4.3900921561153248909886245693114366521619353797757M+0
J = 13 f(x) = -1.7323119072M-7 x:
4.3900776381063320867951914980063629286730825522973M+0
J = 14 f(x) = -1.9461226903M-12 x:
4.3900776508329989159958480043129330063285601971190M+0
J = 15 f(x) = 1.9182672042M-20 x:
4.3900776508331418921725660042962397803248267899607M+0
J = 16 f(x) = -2.1241838752M-33 x:
4.3900776508331418921711567071874581130384786044923M+0
J = 17 f(x) = -2.3185368313M-54 x:
4.3900776508331418921711567071874582690963097189549M+0
J = 18 f(x) = -1.0000000000M-77 x:
4.3900776508331418921711567071874582690963097189549M+0
J = 19 f(x) = -1.0000000000M-77 x:
4.3900776508331418921711567071874582690963097189549M+0
FM_SECANT. Function 3 19 iterations.
Estimated relative error = 1.138932M-57, Root:
4.3900776508331418921711567071874582690963097189549M+0
Case 4. Find a root between 1 and 2 for f(x) = polygamma(0,x).
Use KPRT = 1, so FM_SECANT will print the result.
FM_SECANT. Function 4 11 iterations.
Estimated relative error = 3.420833M-57, Root:
1.4616321449683623412626595423257213284681962040064M+0
Case 5. Find a root near 3.1 for f(x) = cos(x) + 1. (Double root)
Use KPRT = 2, so FM_SECANT will print the iterations.
FM_SECANT. Begin trace of all iterations.
J = 0 f(AX) = 8.6484972672M-4 x:
3.1000000000000000000000000000000000000000000000000M+0
J = 0 f(BX) = 1.7052242052M-3 x:
3.2000000000000000000000000000000000000000000000000M+0
J = 1 f(x) = 1.0422702438M-2 x:
2.9970875783570827008391241954412154141991368316547M+0
J = 2 f(x) = 4.8078499092M-3 x:
3.2396916589497320151463064609294213432799905009368M+0
J = 3 f(x) = 4.6403965569M-2 x:
3.4474271249802673219623508910459796120747925426733M+0
J = 4 f(x) = 2.7432671392M-3 x:
3.2156807404865076385409933147079484010368360207527M+0
J = 5 f(x) = 1.7712155432M-3 x:
3.2011197677104049910687744827986342665736646250163M+0
J = 6 f(x) = 5.4428436058M-4 x:
3.1745876150836989946718504008020165861243120692951M+0
J = 7 f(x) = 2.2524007549M-4 x:
3.1628175696799296207951052135294249468006868205820M+0
J = 8 f(x) = 8.3403335932M-5 x:
3.1545081090839358367174767078372923961650525112318M+0
J = 9 f(x) = 3.2234635163M-5 x:
3.1496219509866413602496999070622136243836055823282M+0
J = 10 f(x) = 1.2257041924M-5 x:
3.1465438285944167712048011249784096248313251195505M+0
J = 11 f(x) = 1.5313139121M-3 x:
3.1446552790200871817410158401485968932236201175305M+0
J = 12 f(x) = 2.4832118180M-3 x:
3.1465590670175217495090723179227983616801874230198M+0
J = 13 f(x) = 5.0884881537M-9 x:
3.1415926637667695457830203649682113061534827694136M+0
J = 14 f(x) = 1.0459100332M-14 x:
3.1415926535898141566633070137156315280367587416150M+0
J = 15 f(x) = 9.0271675357M-32 x:
3.1415926535897932384626433832796834275478838739507M+0
J = 16 f(x) = 3.2916898334M-60 x:
3.1415926535897932384626433832795028841971693993751M+0
J = 17 f(x) = 5.0068598259M-79 x:
3.1415926535897932384626433832795028841971693993751M+0
J = 18 f(x) = 5.0068598259M-79 x:
3.1415926535897932384626433832795028841971693993751M+0
FM_SECANT. Function 5 18 iterations.
Estimated relative error = 1.591549M-57, Root:
3.1415926535897932384626433832795028841971693993751M+0
Case 6. Find a root near 3.1 for f(x) = cos(x) + 1 - 1.0E-40.
There are two different roots that agree to about 20 digits,
so here the convergence is slower.
Use KPRT = 1, so FM_SECANT will print the result.
FM_SECANT. Function 6 54 iterations.
Estimated relative error = 1.591549M-57, Root:
3.1415926535897932384767855189032338346851862866172M+0
Case 7. Find a root near 3.1 for f(x) = sin(x)**3. (Triple root)
Use KPRT = 2, so FM_SECANT will print the iterations.
FM_SECANT. Begin trace of all iterations.
J = 0 f(AX) = 7.1890948202M-5 x:
3.1000000000000000000000000000000000000000000000000M+0
J = 0 f(BX) = -1.9891226494M-4 x:
3.2000000000000000000000000000000000000000000000000M+0
J = 1 f(x) = 3.4053191807M-6 x:
3.1265473025109802113579063768052712098830330073810M+0
J = 2 f(x) = -4.6033019682M-3 x:
3.1277836254965637319671255990161395030696935340751M+0
J = 3 f(x) = -5.0151907695M-3 x:
3.1265482164119758136089201494691601198372701516572M+0
J = 4 f(x) = -6.6600352394M-7 x:
3.1415906555792214179684872785638182310056451601383M+0
J = 5 f(x) = -5.0254086750M-11 x:
3.1415926534390309782133329510918323393079713387829M+0
J = 6 f(x) = -6.6877258692M-23 x:
3.1415926535897932384624427515034254892529502674081M+0
J = 7 f(x) = -5.0669018059M-43 x:
3.1415926535897932384626433832795028841971678793046M+0
J = 8 f(x) = 3.3379065506M-79 x:
3.1415926535897932384626433832795028841971693993751M+0
J = 9 f(x) = 3.3379065506M-79 x:
3.1415926535897932384626433832795028841971693993751M+0
FM_SECANT. Function 7 9 iterations.
Estimated relative error = 1.591549M-57, Root:
3.1415926535897932384626433832795028841971693993751M+0
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