Лаб1Апр2008 (Теория к лабам 19 страниц по БВМиС. 46 страниц теория дальнейших лекций), страница 6

0.960000 0.975000

0.200000 0.992000

0.020000 0.099200

0.150000 0.744000

0.006000 0.029400

0.100800 0.971985

0.155975 0.773376

0.058014 0.559814

0.076752 0.380707

0.134766 0.940521

9.6000E-0004 9.6000E-0004

1.4038E+0002 9.7971E+0002

1.4048E+0002 9.7982E+0002

7.0573E-0004 1.0794E-0004

K= 15 EF= 0.0004068329

Метод ступенчатого масштабирования (программа STEP),

Получение зависимости погрешности вычислений

от длины разрядной сетки.

program step;

var

X,Y,W,Z:real;

N,k,i:integer;

AM,BM,XM,YM,WM,ZM,DM,EM,GM,HM,FM:REAL;

SF,SF1,F,FP,ESUM,ESI,ES1,ES2,ESM:REAL;

const

a=2.4;b=0.65;

x1=50.0;x2=248.0;y1=5.0;y2=24.8;w1=50.0;w2=248.0;z1=2.0;z2=9.8;

sa=0.4;sb=1.5;sd=0.004;se=0.003;

sk1=0.8;sk2=0.6;

{$I func.pas}

begin

N:=20;

AM:=A*SA;

BM:=B*SB;

SF:=SD*SA*SK2;

SF1:=SE/SB*SK1*SK2;

for k:=9 to 29 do

begin

Randomize;

ES1:=1;

ES2:=-1;

ESM:=0;

ESUM:=0;

for i:=0 to N do

begin

X:=x1+(Random(10000)/10000)*(x2-x1);

Y:=y1+(Random(10000)/10000)*(y2-y1);

Z:=z1+(Random(10000)/10000)*(z2-z1);

W:=w1+(Random(10000)/10000)*(w2-w1);

XM:=X*SD;

YM:=Y*SD;

WM:=W*SE;

ZM:=Z*SE;

DM:=SUF(k,XM,YM);

EM:=ADF(k,WM,ZM);

GM:=FMU(k,FMU(k,DM,AM),SK2);

HM:=FMU(k,FMU(k,DIF(k,EM,BM),SK1),SK2);

FM:=ADF(k,GM,HM);

F:=FM/SF;

FP:=(X-Y)*A+(W+Z)/B;

ESI:=ABS((F-FP)/FP);

if ESI

if ESI>ES2 then ES2:=ESI;

ESUM:=ESUM+ESI;

end;

ESM:=ESUM/N;

writeln('K=',k:3,' ES1=',ES1:13,' ES2=',ES2:13,' ESM=',ESM:13);

end;

end.

K= 9 ES1= 4.9364E-0003 ES2= 2.0139E-0002 ESM= 1.1914E-0002

K= 10 ES1= 2.4526E-0003 ES2= 8.2623E-0003 ESM= 5.0485E-0003

K= 11 ES1= 1.6402E-0003 ES2= 4.2995E-0003 ESM= 2.7767E-0003

K= 12 ES1= 6.4249E-0004 ES2= 2.3238E-0003 ESM= 1.3484E-0003

K= 13 ES1= 3.8842E-0004 ES2= 1.1717E-0003 ESM= 6.5880E-0004

K= 14 ES1= 1.8861E-0004 ES2= 5.7311E-0004 ESM= 3.3743E-0004

K= 15 ES1= 1.0482E-0004 ES2= 2.9363E-0004 ESM= 1.8130E-0004

K= 16 ES1= 4.9524E-0005 ES2= 1.8451E-0004 ESM= 9.3395E-0005

K= 17 ES1= 2.0977E-0005 ES2= 8.6393E-0005 ESM= 4.9431E-0005

K= 18 ES1= 1.0672E-0005 ES2= 6.0172E-0005 ESM= 2.3877E-0005

K= 19 ES1= 6.1717E-0006 ES2= 2.3532E-0005 ESM= 1.2595E-0005

K= 20 ES1= 3.2423E-0006 ES2= 1.0087E-0005 ESM= 6.2509E-0006

K= 21 ES1= 1.3973E-0006 ES2= 7.5016E-0006 ESM= 3.2839E-0006

K= 22 ES1= 7.0917E-0007 ES2= 2.9215E-0006 ESM= 1.3723E-0006

K= 23 ES1= 4.3439E-0007 ES2= 1.7765E-0006 ESM= 8.3001E-0007

K= 24 ES1= 1.5913E-0007 ES2= 9.1776E-0007 ESM= 3.8206E-0007

K= 25 ES1= 6.3950E-0008 ES2= 3.6001E-0007 ESM= 1.9776E-0007

K= 26 ES1= 4.1267E-0008 ES2= 2.0212E-0007 ESM= 9.1352E-0008

K= 27 ES1= 3.3080E-0008 ES2= 1.0131E-0007 ESM= 5.6052E-0008

K= 28 ES1= 1.5741E-0008 ES2= 4.3851E-0008 ESM= 2.6832E-0008

K= 29 ES1= 4.7824E-0009 ES2= 3.2155E-0008 ESM= 1.2020E-0008

Приложение 3

Метод переменных масштабов (программа VAR).

program vara;

var

k:integer;

AM,BM,X1M,X2M,Y1M,Y2M,W1M,W2M,Z1M,Z2M,D1M,D2M,E1M,E2M,G1M,G2M,H1M,H2M,

F1M,F2M:real;

SF,SF1,SF2,SF3,F1,F2,F1P,F2P,EF1,EF2,EF:real;

const

a=2.4;b=0.65;x1=50.0;x2=248.0;y1=5.0;y2=24.8;

w1=50.0;w2=248.0;z1=2.0;z2=9.8;

sa=0.4;sb=1.53;sx=0.004;sy=0.04;sw=0.004;sz=0.1;

sk1=0.1;sk2=0.04;sk3=0.9;sk4=0.68;sk5=0.6;

{$I func.pas}

begin

k:=15;

AM:=A*SA; BM:=B*SB;

X1M:=X1*SX; X2M:=X2*SX;

Y1M:=Y1*SY; Y2M:=Y2*SY;

W1M:=W1*SW; W2M:=W2*SW;

Z1M:=Z1*SZ; Z2M:=Z2*SZ;

D1M:=SUF(k,X1M,FMU(k,Y2M,SK1));

D2M:=SUF(k,X2M,FMU(k,Y1M,SK1));

E1M:=ADF(k,FMU(k,W1M,SK3),FMU(k,FMU(k,Z1M,SK2),SK3));

E2M:=ADF(k,FMU(k,W2M,SK3),FMU(k,FMU(k,Z2M,SK2),SK3));

G1M:=FMU(k,D1M,AM);

G2M:=FMU(k,D2M,AM);

H1M:=DIF(k,E1M,BM);

H2M:=DIF(k,E2M,BM);

F1M:=ADF(k,FMU(k,G1M,SK5),FMU(k,FMU(k,H1M,SK4),SK5));

F2M:=ADF(k,FMU(k,G2M,SK5),FMU(k,FMU(k,H2M,SK4),SK5));

wri(am,bm);wri(x1m,x2m);

wri(y1m,y2m);wri(w1m,w2m);

wri(z1m,z2m);wri(d1m,d2m);

wri(e1m,e2m);wri(g1m,g2m);

wri(h1m,h2m);wri(f1m,f2m);

SF:=SX*SA*SK5;

SF1:=SY*SK1*SA*SK5;

SF2:=SW*SK3/SB*SK4*SK5;

SF3:=SZ*SK2*SK3/SB*SK4*SK5;

F1:=F1M/SF;

F2:=F2M/SF;

F1P:=(X1-Y2)*A+(W1+Z1)/B;

F2P:=(X2-Y1)*A+(W2+Z2)/B;

EF1:=ABS((F1-F1P)/F1P);

EF2:=ABS((F2-F2P)/F2P);

writ(SF,SF1);

writ(SF2,SF3);

writ(F1,F2);

writ(F1P,F2P);

writ(EF1,EF2);

ef:=0.5*(ef1+ef2);

writeln('K=',k:3,' EF=',ef:17:10);

end.

0.960000 0.994500

0.200000 0.992000

0.200000 0.992000

0.200000 0.992000

0.200000 0.980000

0.100830 0.971985

0.187103 0.927979

0.096771 0.933075

0.188141 0.933105

0.134796 0.940491

9.6000E-0004 9.6000E-0004

9.6000E-0004 9.6000E-0004

1.4041E+0002 9.7968E+0002

1.4048E+0002 9.7982E+0002

4.7944E-0004 1.4038E-0004

K= 15 EF= 0.0003099101

Метод переменных масштабов (программа VAR),

Получение зависимости погрешности вычислений

от длины разрядной сетки.

program vara;

var

X,Y,W,Z,alpha:real;

N,k,i:integer;

AM,BM,XM,YM,WM,ZM,DM,EM,GM,HM,FM:REAL;

SF,SF1,SF2,SF3,F,FP,ESUM,ESI,ES1,ES2,ESM:REAL;

const

a=2.4;b=0.65;

x1=50.0;x2=248.0;y1=5.0;y2=24.8;w1=50.0;w2=248.0;z1=2.0;z2=9.8;

sa=0.4;sb=1.5;sx=0.004;sy=0.04;sw=0.004;sz=0.1;

sk1=0.1;sk2=0.04;sk3=0.96;sk4=0.625;sk5=0.6;

{$I func.pas}

begin

N:=20;

AM:=A*SA;

BM:=B*SB;

SF:=SX*SA*SK5;

SF1:=SY*SK1*SA*SK5;

SF2:=SW*SK3/SB*SK4*SK5;

SF3:=SZ*SK2*SK3/SB*SK4*SK5;

for k:=9 to 29 do

begin

Randomize;

ES1:=1;

ES2:=-1;

ESM:=0;

ESUM:=0;

for i:=0 to N do

begin

X:=x1+(Random(10000)/10000)*(x2-x1);

Y:=y1+(Random(10000)/10000)*(y2-y1);

Z:=z1+(Random(10000)/10000)*(z2-z1);

W:=w1+(Random(10000)/10000)*(w2-w1);

XM:=X*SX;

YM:=Y*SY;

WM:=W*SW;

ZM:=Z*SZ;

DM:=SUF(k,XM,FMU(k,YM,SK1));

EM:=ADF(k,FMU(k,WM,SK3),FMU(k,FMU(k,ZM,SK2),SK3));

GM:=FMU(k,DM,AM);

HM:=DIF(k,EM,BM);

FM:=ADF(k,FMU(k,GM,SK5),FMU(k,FMU(k,HM,SK4),SK5));

F:=FM/SF;

FP:=(X-Y)*A+(W+Z)/B;

ESI:=ABS((F-FP)/FP);

if ESI

if ESI>ES2 then ES2:=ESI;

ESUM:=ESUM+ESI;

end;

ESM:=ESUM/N;

writeln('K=',k:3,' ES1=',ES1:13,' ES2=',ES2:13,' ESM=',ESM:13);

end;

end.

K= 9 ES1= 7.1086E-0003 ES2= 2.1892E-0002 ESM= 1.2927E-0002

K= 10 ES1= 3.1311E-0003 ES2= 1.7486E-0002 ESM= 7.0179E-0003

K= 11 ES1= 1.3707E-0003 ES2= 6.4712E-0003 ESM= 3.3373E-0003

K= 12 ES1= 7.4389E-0004 ES2= 3.1667E-0003 ESM= 1.6734E-0003

K= 13 ES1= 2.6654E-0004 ES2= 2.0653E-0003 ESM= 8.0128E-0004

K= 14 ES1= 2.0512E-0004 ES2= 9.6380E-0004 ESM= 4.3008E-0004

K= 15 ES1= 1.2176E-0004 ES2= 3.7254E-0004 ESM= 2.1626E-0004

K= 16 ES1= 5.6231E-0005 ES2= 1.7620E-0004 ESM= 1.0530E-0004

K= 17 ES1= 1.7439E-0005 ES2= 1.1551E-0004 ESM= 5.2626E-0005

K= 18 ES1= 1.1254E-0005 ES2= 5.4829E-0005 ESM= 2.6283E-0005

K= 19 ES1= 7.8331E-0006 ES2= 2.5829E-0005 ESM= 1.3253E-0005

K= 20 ES1= 3.9137E-0006 ES2= 1.3109E-0005 ESM= 6.9689E-0006

K= 21 ES1= 1.5447E-0006 ES2= 7.4200E-0006 ESM= 3.6440E-0006

K= 22 ES1= 9.1716E-0007 ES2= 3.2403E-0006 ESM= 1.7248E-0006

K= 23 ES1= 5.1101E-0007 ES2= 1.7309E-0006 ESM= 9.0149E-0007

K= 24 ES1= 1.9655E-0007 ES2= 7.8269E-0007 ESM= 4.1636E-0007

K= 25 ES1= 1.2559E-0007 ES2= 4.2712E-0007 ESM= 2.2625E-0007

K= 26 ES1= 4.7674E-0008 ES2= 1.5270E-0007 ESM= 9.6526E-0008

K= 27 ES1= 3.3470E-0008 ES2= 9.3181E-0008 ESM= 5.4460E-0008

K= 28 ES1= 1.3435E-0008 ES2= 4.8538E-0008 ESM= 2.8691E-0008

K= 29 ES1= 5.8550E-0009 ES2= 2.6216E-0008 ESM= 1.3037E-0008

Приложение 4

Номера индивидуальных заданий (М - последняя цифра номера группы; I - номер студента по списку в журнале)

Приложение 5