Математика \ Вычислительная математика

Решение нелинейного алгебраического уравнения с действительными коэффициентами вида a1+a2x+a3x2+...+x6=0, страница 2

      real*8 esp,ess(9),ai(7),a(7),b(7),em,emo,eso,al(6),be(6)

      complex*16 z(6),zk(6)

      data ess/0.000000001,0.00000001,0.0000001,0.000001,0.00001,0.0001,

     *         0.001,0.01,0.1/

      esp=1.d-3

      n=6

      n1=n+1

      do 101 ii=1,8

      print*,'  al ->'

      read*,(al(k),k=1,n)

      print*,'  be ->'

      read*,(be(k),k=1,n)

      call n1yfu(n,al,be,z,n1,ai)

      call n1ymsd(n,n1,ai,a,b,zk,esp,kmo,km)

      call n1yem(z,zk,n,em,emo,eso)

      write (*,103) ii,em,emo,eso,km,kmo

      write (22,103) ii,em,emo,eso,km,kmo

101   continue

103   format (2x,i2,3(2x,e11.4),2(2x,i3))

      do 2 i=1,7

      write(1,*)ai(i)

2     continue

      write(1,*) ' '

      do 3 i=1,6

      write(1,*) z(i)

3     continue

      write(1,*)' '

      do 4 i=1,6

      write(1,*) zk(i)

4     continue

      write(1,*)' '

      write(1,*)em,emo,eso

      write(1,*)km,kmo

      stop

      end

5.Результаты вычислений

Для корней вида 1:

               Порядок алгебраического уравнения N = 6.

  Параметр  останова  EPS = 0,1D–6.

               Коэффициенты алгебраического уравнения:

A(1)=

112896,00000000000000000

A(2)=

-28224,00000000000000000

A(3)=

-3676,00000000000000000

A(4)=

1360,00000000000000000

A(5)=

-21,00000000000000000

A(6)=

-16,00000000000000000

A(7)=

1,00000000000000000

               Корни уравнения и их оценки:

XI(1) =

-7,00000000000000000;   0,00000000000000000E-01

XI(1) =

-6,99999999999999911;   0,00000000000000000E-01

XI(2) =

-6,00000000000000000;   0,00000000000000000E-01

XI(2) =

-6,00000000000000000;   0,00000000000000000E-01

XI(3) =

6,00000000000000000;   0,00000000000000000E-01

XI(3) =

6,00000000000001243;   0,00000000000000000E-01

XI(4) =

7,00000000000000000;   0,00000000000000000E-01

XI(4) =

6,99999999999997424;   0,00000000000000000E-01

XI(5) =

8,00000000000000000;   0,00000000000000000E-01

XI(5) =

7,99999998985375171;   0,00000000000000000E-01

XI(6) =

8,00000000000000000;   0,00000000000000000E-01

XI(6) =

8,00000001014626072;   0,00000000000000000E-01

Погрешности  Eм=0,1269E-02,  Eмо=0,1587E-03,  Eсо=0,1039E-03

               Макс, кол–во итераций на один корень  KM = 26

               Общее кол–во итераций  KMO = 79

Для корней вида 2:

               Порядок алгебраического уравнения N = 6

  Параметр  останова  EPS = 0,1D–6

               Коэффициенты алгебраического уравнения:

A(1)=

903168,00000000000000000

A(2)=

166656,00000000000000000

A(3)=

15376,00000000000000000

A(4)=

104,00000000000000000

A(5)=

50,00000000000000000

A(6)=

10,00000000000000000

A(7)=

1,00000000000000000

               Корни уравнения и их оценки:

XI(1) =

-7,00000000000000000;       7,00000000000000000

XI(1) =

-7,00000000000000000;       7,00000000000000000

XI(2) =

-7,00000000000000000;      -7,00000000000000000

XI(2) =

-7,00000000000000000;      -7,00000000000000000

XI(3) =

-6,00000000000000000;       6,00000000000000000

XI(3) =

-6,00000000000000000;       6,00000000000000000

XI(4) =

-6,00000000000000000;      -6,00000000000000000

XI(4) =

-6,00000000000000000;      -6,00000000000000000

XI(5) =

8,00000000000000000;       8,00000000000000000

XI(5) =

8,00000000000000000;       8,00000000000000000

XI(6) =

8,00000000000000000;      -8,00000000000000000

XI(6) =

8,00000000000000000;      -8,00000000000000000

Погрешности  Eм=0,5610E-08,  Eмо=0,9350E-09,  Eсо = 0,3816E-09

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