Duritelfa Solution equations

Try compiling the following subroutine:

(1) Realizing matrix triangular decomposition a=lu;

(2) using decomposition factor l,u to solve the ax=b of the equation group (that is, solving the ly=b and then solving ux=y).

Using the above subroutine to solve the linear equation Group AX=BK (k=1,2,...,10), where

A=1 2 4 7 11 16

2 3 5 8 12 17

4 5 6 9 13 18

7 8 9 10 14 19

11 12 13 14 15 20

16 17 18 19 20 21

The B1 is a non-zero six-element vector; If Xk is a ax= BK solution vector, take bk+1=xk/| | xk| |. Please output the result: L;u;bk;xk (k=1,2,...,10). And observe carefully, can find what interesting phenomenon.

Or the calculation method of the work, according to the book formula and flowchart to achieve

Input

6
1 2 4 7 11 16
2 3 5 8 12 17
4 5 6 9 13 18
7 8 9 10 14 19
11 12 13 14 15 20
16 17 18 19 20 21

b Vector any: 6 x 1.

1 1 1 1 1 1

#include <iostream> #include <stdio.h> #include <iomanip> #include <math.h>using namespace std; const int Maxn=1000;int n;double A[MAXN][MAXN];d ouble B[MAXN];d ouble X[MAXN];d ouble y[maxn];//double L[MAXN][MAXN];//    Double u[maxn][maxn];void Inita () {printf ("Order of input matrix A:");    cin>>n;    printf ("Input matrix a\n");        for (int i=1;i<=n;i++) {for (int j=1;j<=n;j++) {cin>>a[i][j];    }}}void INITB () {printf ("Input b vector \ n");    for (int i=1;i<=n;i++) {cin>>b[i];    }}void Duliteer () {//Compact format gets a=lu double sum;    for (int i=2;i<=n;i++) {a[i][1]=a[i][1]/a[1][1];            } for (int k=2;k<=n;k++) {for (int i=k;i<=n;i++) {sum=0;            for (int j=1;j<=k-1;j++) {sum+=a[k][j]*a[j][i];        } a[k][i]=a[k][i]-sum;            } for (int i=k+1;i<=n;i++) {sum=0;            for (int j=1;j<=k-1;j++) {sum+=a[i][j]*a[j][k];       }     a[i][k]= (a[i][k]-sum)/a[k][k];    }}}void gety () {y[1]=b[1];    Double sum;        for (int k=2;k<=n;k++) {sum=0;        for (int j=1;j<=k-1;j++) {sum+=a[k][j]*y[j];    } y[k]=b[k]-sum;    }}void Getx () {double sum,m;    X[n]=y[n]/a[n][n];    X[0]=fabs (X[n]);        for (int k=n-1;k>=1;k--) {sum=0;        for (int j=k+1;j<=n;j++) {sum+=a[k][j]*x[j];        } x[k]= (Y[k]-sum)/a[k][k];    X[0]=max (X[0],fabs (x[k));    }}void Xianshi () {cout<<endl;    printf ("L and U respectively: \ n"); for (int i=1;i<=n;i++) {for (int j=1;j<=n;j++) {if (i==j) {COUT&LT;&LT;SETW (5) <<                1;            cout<< "";        } COUT&LT;&LT;SETW (5) <<A[i][j]<< "";    } cout<<endl;    }}void output () {printf ("b vector: \ n");    for (int i=1;i<=n;i++) {cout<<b[i]<< "";    } cout<<endl;    printf ("x vector: \ n"); for (int i=1;i<=n;i++) {cout<<x[i]<< ""; } Cout<<endl;}        int main () {while (1) {Inita ();        INITB ();        Duliteer ();        Gety ();        Getx ();        Xianshi ();            for (int i=1;i<=10;i++) {cout<<endl;            printf ("(%d): \ n", i);            Output ();            for (int j=1;j<=n;j++) {b[j]=x[j]/x[0];            } gety ();        Getx ();    } cout<<endl; } return 0;}

Duritelfa Solution equations