ЧМ ЛР1
.docxЛР 1. Распространение ошибок в вычислительных процедурах.
>> p=poly(1:20)
p = 1.0e+019 *
0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000
0.0000 -0.0000 0.0000 -0.0000 0.0001 -0.0010
0.0063 -0.0311 0.1207 -0.3600 0.8038 -1.2871
1.3804 -0.8753 0.2433
>> roots(p)
ans = 20.0003 18.9972 18.0112 16.9711 16.0483 14.9354 14.0653 12.9491 12.0334
10.9840 10.0061 8.9984 8.0003 7.0000 6.0000 5.0000 4.0000 3.0000 2.0000
1.0000
>> p(2)=p(2)+10^(-7)
>> roots(p)
ans =
20.4220 + 0.9992i
20.4220 - 0.9992i
18.1573 + 2.4702i
18.1573 - 2.4702i
15.3150 + 2.6988i
15.3150 - 2.6988i
12.8466 + 2.0627i
12.8466 - 2.0627i
10.9213 + 1.1037i
10.9213 - 1.1037i
9.5678
9.1137
7.9941
7.0002
6.0000
5.0000
4.0000
3.0000
2.0000
1.0000
>> 2^1023
ans =
8.9885e+307
>> 2^1024
ans = Inf
>> realmax
ans = 1.7977e+308
>> realmin
ans = 2.2251e-308
>> format long e
>> sqrt(2)
ans = 1.414213562373095e+000
15 знаков после запятой
>> format long g
>> sqrt(2)
ans = 1.4142135623731
13 знаков после запятой
c = 1;
for r = 1:10^8
c = c+10^-16
end
c = 1
for n = 50:55
n
e = 2^(-n)
c = (1+e-1)/e
end
n = 50
e = 8.881784197001252e-016
c = 1
n = 51
e = 4.440892098500626e-016
c = 1
n = 52
e = 2.220446049250313e-016
c = 1
n = 53
e = 1.110223024625157e-016
c = 0
n = 54
e = 5.551115123125783e-017
c = 0
n = 55
e = 2.775557561562891e-017
c = 0
При n = 53.
I = 1/exp(1)
for n = 1:30
I = 1-n*I
end
I = 0.3679
I = 0.6321
I = -0.2642
I = 1.7927
I = -6.1709
I = 31.8545
I = -190.1268
I = 1.3319e+003
I = -1.0654e+004
I = 9.5888e+004
I = -9.5888e+005
I = 1.0548e+007
I = -1.2657e+008
I = 1.6454e+009
I = -2.3036e+010
I = 3.4554e+011
I = -5.5287e+012
I = 9.3987e+013
I = -1.6918e+015
I = 3.2144e+016
I = -6.4287e+017
I = 1.3500e+019
I = -2.9701e+020
I = 6.8312e+021
I = -1.6395e+023
I = 4.0987e+024
I = -1.0657e+026
I = 2.8773e+027
I = -8.0564e+028
I = 2.3364e+030
I = -7.0091e+031
n = 0;
x = 0;
u = x;
s = u;
while abs(u) >= 10^-17
u = u*(-x^2)/((2*n+2)*(2*n+3));
s = s + u
n = n+1
end
s = 0
x = pi/3;
s = 8.660254037844385e-01
n = 9
x = pi/2;
s = 1.000000000000000e+00
n = 10
x = pi;
s = 2.479031568558660e-16
n = 14
x = 2*pi;
s = 4.372518090456442e-16
n = 20
x = 12*pi;
s = -8.892108572083269e+03
n = 1
s = 6.256703097986762e+05
n = 2
s = -2.084706124603431e+07
n = 3
s = 4.030076704876848e+08
n = 4
s = -5.073284217755948e+09
n = 5
s = 4.481794764857572e+10
n = 6
s = -2.928323757368300e+11
n = 7
s = 1.471419157170500e+12
n = 8
s = -5.860144924434060e+12
n = 9
s = 1.894887351899670e+13
n = 10
s = -5.073323805551464e+13
n = 11
s = 1.143231319620046e+14
n = 12
s = -2.198391400283014e+14
n = 13
s = 3.650366210125239e+14
n = 14
s = -5.287686515437110e+14
n = 15
s = 6.741637736932740e+14
n = 16
s = -7.625045210964858e+14
n = 17
s = 7.703979356778448e+14
n = 18
s = -6.996400400780053e+14
n = 19
s = 5.742940036058568e+14
n = 20
s = -4.282222789913373e+14
n = 21
s = 2.913732930002998e+14
n = 22
s = -1.816636181486192e+14
n = 23
s = 1.041743724729983e+14
n = 24
s = -5.513524956395159e+13
n = 25
s = 2.701805389686622e+13
n = 26
s = -1.229446030439037e+13
n = 27
s = 5.209252320208574e+12
n = 28
s = -2.060379344999167e+12
n = 29
s = 7.625080783673730e+11
n = 30
s = -2.646175303861090e+11
n = 31
s = 8.628981906629321e+10
n = 32
s = -2.649118675829393e+10
n = 33
s = 7.670570114717724e+09
n = 34
s = -2.098338485186934e+09
n = 35
s = 5.431755781407018e+08
n = 36
s = -1.332533643446914e+08
n = 37
s = 3.102489843043509e+07
n = 38
s = -6.864756065113947e+06
n = 39
s = 1.445375062997742e+06
n = 40
s = -2.899393320672414e+05
n = 41
s = 5.547646472214494e+04
n = 42
s = -1.013605687910572e+04
n = 43
s = 1.770228488944267e+03
n = 44
s = -2.958871412822286e+02
n = 45
s = 4.731191482845196e+01
n = 46
s = -7.308735082871102e+00
n = 47
s = 1.027618629837484e+00
n = 48
s = -1.935541091901418e-01
n = 49
s = -2.171660177409968e-02
n = 50
s = -4.496231123564980e-02
n = 51
s = -4.193691400828946e-02
n = 52
s = -4.231601506857765e-02
n = 53
s = -4.227024653655223e-02
n = 54
s = -4.227557391508915e-02
n = 55
s = -4.227497566974416e-02
n = 56
s = -4.227504052405873e-02
n = 57
s = -4.227503373269079e-02
n = 58
s = -4.227503442006073e-02
n = 59
s = -4.227503435278070e-02
n = 60
s = -4.227503435915281e-02
n = 61
s = -4.227503435856854e-02
n = 62
s = -4.227503435862043e-02
n = 63
s = -4.227503435861596e-02
n = 64
s = -4.227503435861633e-02
n = 65
s = -4.227503435861631e-02
n = 66
s = -4.227503435861631e-02
x = 13*pi;
s = -1.131262427327312e+04
n = 1
s = 9.355454325849062e+05
n = 2
s = -3.666741507299782e+07
n = 3
s = 8.344485879892408e+08
n = 4
s = -1.237454583990469e+10
n = 5
s = 1.288569661612276e+11
n = 6
s = -9.928999707853949e+11
n = 7
s = 5.885957481828991e+12
n = 8
s = -2.766281650152009e+13
n = 9
s = 1.055707990303114e+14
n = 10
s = -3.336164741321313e+14
n = 11
s = 8.872971672911935e+14
n = 12
s = -2.013613025924397e+15
n = 13
s = 3.945267867808636e+15
n = 14
s = -6.742037195574122e+15
n = 15
s = 1.013867393330813e+16
n = 16
s = -1.352216976739919e+16
n = 17
s = 1.610652035543567e+16
n = 18
s = -1.724001346608160e+16
n = 19
s = 1.667510201394329e+16
n = 20
s = -1.464780088631317e+16
n = 21
s = 1.173878880760396e+16
n = 22
s = -8.618222801835078e+15
n = 23
s = 5.818318474580482e+15
n = 24
s = -3.624669279450516e+15
n = 25
s = 2.090336359492995e+15
n = 26
s = -1.119232250700974e+15
n = 27
s = 5.579112797657878e+14
n = 28
s = -2.595678539731095e+14
n = 29
s = 1.129799782370094e+14
n = 30
s = -4.610759304387691e+13
n = 31
s = 1.767899482406649e+13
n = 32
s = -6.381086051436836e+12
n = 33
s = 2.172052937651884e+12
n = 34
s = -6.984341040911333e+11
n = 35
s = 2.124994176625214e+11
n = 36
s = -6.126698607127130e+10
n = 37
s = 1.676313549986411e+10
n = 38
s = -4.358475484499195e+09
n = 39
s = 1.078263506127876e+09
n = 40
s = -2.541314775247734e+08
n = 41
s = 5.712702747458804e+07
n = 42
s = -1.226186781120111e+07
n = 43
s = 2.515726663338048e+06
n = 44
s = -4.938561128913662e+05
n = 45
s = 9.285182877741579e+04
n = 46
s = -1.673464634788780e+04
n = 47
s = 2.894456053982867e+03
n = 48
s = -4.801697295549866e+02
n = 49
s = 7.713239232666547e+01
n = 50
s = -1.134651489313950e+01
n = 51
s = 2.168096484601136e+00
n = 52
s = 1.806274596816635e-01
n = 53
s = 4.622299981609539e-01
n = 54
s = 4.237613122166869e-01
n = 55
s = 4.288311881921011e-01
n = 56
s = 4.281861564399618e-01
n = 57
s = 4.282654291476791e-01
n = 58
s = 4.282560128284382e-01
n = 59
s = 4.282570945139371e-01
n = 60
s = 4.282569742812605e-01
n = 61
s = 4.282569872195620e-01
n = 62
s = 4.282569858709424e-01
n = 63
s = 4.282569860071735e-01
n = 64
s = 4.282569859938307e-01
n = 65
s = 4.282569859950983e-01
n = 66
s = 4.282569859949814e-01
n = 67
s = 4.282569859949918e-01
n = 68
s = 4.282569859949910e-01
n = 69
s = 4.282569859949910e-01
n = 70
s = 4.282569859949910e-01
x = 14*pi;
s = -1.413622157130686e+04
n = 1
s = 1.357403203011686e+06
n = 2
s = -6.181317065560374e+07
n = 3
s = 1.635406835730075e+09
n = 4
s = -2.821163360744844e+10
n = 5
s = 3.418997921401632e+11
n = 6
s = -3.067430007215116e+12
n = 7
s = 2.117945356972041e+13
n = 8
s = -1.159673334983215e+14
n = 9
s = 5.157054486812840e+14
n = 10
s = -1.899185168562680e+15
n = 11
s = 5.886593085710126e+15
n = 12
s = -1.556802238374605e+16
n = 13
s = 3.554370074822538e+16
n = 14
s = -7.077101706234550e+16
n = 15
s = 1.239824910186598e+17
n = 16
s = -1.926052869433913e+17
n = 17
s = 2.671701190883284e+17
n = 18
s = -3.329709529043357e+17
n = 19
s = 3.749182990596908e+17
n = 20
s = -3.833159356174575e+17
n = 21
s = 3.574721957798840e+17
n = 22
s = -3.053455734963125e+17
n = 23
s = 2.398001909010692e+17
n = 24
s = -1.737500502613613e+17
n = 25
s = 1.165217737330744e+17
n = 26
s = -7.254022695214874e+16
n = 27
s = 4.203670355917986e+16
n = 28
s = -2.273316190459337e+16
n = 29
s = 1.150005614209720e+16
n = 30
s = -5.453909710802314e+15
n = 31
s = 2.429857466012196e+15
n = 32
s = -1.018965236879856e+15
n = 33
s = 4.029335445566098e+14
n = 34
s = -1.505033528979399e+14
n = 35
s = 5.318611339071341e+13
n = 36
s = -1.780948170403523e+13
n = 37
s = 5.658887026278758e+12
n = 38
s = -1.708560068851166e+12
n = 39
s = 4.908076011917217e+11
n = 40
s = -1.343099732764403e+11
n = 41
s = 3.505332926938293e+10
n = 42
s = -8.734904365086449e+09
n = 43
s = 2.080445290858248e+09
n = 44
s = -4.740933687842288e+08
n = 45
s = 1.034671800236508e+08
n = 46
s = -2.164565876070841e+07
n = 47
s = 4.344846819465920e+06
n = 48
s = -8.372947615568284e+05
n = 49
s = 1.552354088991652e+05
n = 50
s = -2.751659063967955e+04
n = 51
s = 4.857331341590296e+03
n = 52
s = -6.642247650844893e+02
n = 53
s = 2.431089583656177e+02
n = 54
s = 9.935917274701703e+01
n = 55
s = 1.213310192460855e+02
n = 56
s = 1.180889694482347e+02
n = 57
s = 1.185510648501556e+02
n = 58
s = 1.184874060432011e+02
n = 59
s = 1.184958870555491e+02
n = 60
s = 1.184947937575075e+02
n = 61
s = 1.184949302040982e+02
n = 62
s = 1.184949137094051e+02
n = 63
s = 1.184949156418200e+02
n = 64
s = 1.184949154223164e+02
n = 65
s = 1.184949154465029e+02
n = 66
s = 1.184949154439165e+02
n = 67
s = 1.184949154441850e+02
n = 68
s = 1.184949154441580e+02
n = 69
s = 1.184949154441606e+02
n = 70
s = 1.184949154441604e+02
n = 71
s = 1.184949154441604e+02
n = 72
s = 1.184949154441604e+02
n = 73
s = 1.184949154441604e+02
n = 74
s = 1.184949154441604e+02
n = 75
s = 1.184949154441604e+02