迭代法解线性方程组(C语言描述)

用Gauss-Seidel迭代法解线性方程组的C语言源代码：#include<stdio.h>
#include<math.h>
#include<stdlib.h>
struct Line{
int L;
struct Row *head;
struct Line *next;
};
struct Row{
int R;
float x;
struct Row *link;
};
//建立每次迭代结果的数据存储单元
struct Term{
float x;
float m;
};
struct Line *Create(int Line,int Row){
struct Line *Lhead=NULL,*p1=NULL,*p2=NULL; struct Row*Rhead=NULL,*ptr1,*ptr2=NULL;
int i=1,j=1;
float X;
while(i<=Line){
while(j<=Row+1){
scanf("%f",&X);
if(X!=0||j==Row+1){
ptr1=(struct Row*)malloc(sizeof(Row));
if(ptr1==NULL){
printf("内存分配错误!\n");
exit(1);
}
ptr1->x=X;
ptr1->R=j;
if(ptr2==NULL){
ptr2=ptr1;
Rhead=ptr1;
}
else{
ptr2->link=ptr1;
ptr2=ptr1;
}
}
j++;
}
if(ptr2!=NULL){
ptr2->link=NULL;
ptr2=NULL;
}
if(Rhead!=NULL){
p1=(struct Line*)malloc(sizeof(Line));
if(p1==NULL){
printf("内存分配错误!\n");
exit(1);
}
p1->L=i;
p1->head=Rhead;
if(p2==NULL){
Lhead=p1;
p2=p1;
}
else{
p2->next=p1;
p2=p1;
}
}
i++;
Rhead=NULL;
j=1;
}
if(p2!=NULL)
p2->next=NULL;
return Lhead;
}
struct Line *Change(struct Line*Lhead,int n){ struct Line*p1,*p2,*p3,*p;
struct Row*ptr;
int i=1,k,j;
float max,t;
if(Lhead==NULL){
printf("链表为空!\n");
exit(1);
}
p2=Lhead;
while(i<=n){
max=0;
k=0;
t=0;
ptr=p2->head;
while(ptr!=NULL){
if(ptr->R!=n+1){
t+=fabs(ptr->x);
if(max<fabs(ptr->x)){
max=fabs(ptr->x);
k=ptr->R;
}
}
ptr=ptr->link;
}
t=t-max;
if(max<=t){
printf("系数矩阵A不具有严格对角优势，该程序不能用Gauss-Jacobi迭代法解该方程组!\n");
return NULL;
}
if(p2->L==k)
p2=p2->next;
else if(p2->L>k){
printf("系数矩阵A不具有严格对角优势，该程序不能用Gauss-Jacobi迭代法解该方程组!\n");
exit(0);
}
else{
p3=Lhead;
while(p3->L!=k)
p3=p3->next;
ptr=p3->head;
p3->head=p2->head;
p2->head=ptr;
}
i++;
}
return Lhead;
}
void Deal(struct Line *Lhead,float e,int N,int n){
struct Term*ptr;
struct Line*p1;
struct Row*current;
float m=0,a,b,c=0;
int k=0;
if(Lhead==NULL){
printf("链表为空\n");
exit(1);
}
ptr=(Term*)malloc(n*sizeof(Term));
for(int i=0;i<n;i++){
(ptr+i)->x=0;
(ptr+i)->m=0;
}
printf("迭代过程的数据变化表如下：\n");
printf(" K");
for(int i=1;i<=n;i++)
printf(" X%d",i);
printf("\n %d",k);
for(int i=0;i<n;i++)
printf(" %.5f",ptr[i].x);
printf("\n");
do{
m=0;
p1=Lhead;
while(p1!=NULL){
current=p1->head;
while(current!=NULL){
if(current->link==NULL)
b=current->x;
else if(current->R==p1->L)
a=current->x;
else c+=(current->x)*ptr[(current->R)-1].x;
current=current->link;
}
ptr[(p1->L)-1].m=(b-c)/a-ptr[(p1->L)-1].x;
if(m<fabs(ptr[(p1->L)-1].m))
m=fabs(ptr[(p1->L)-1].m);
ptr[(p1->L)-1].x=(b-c)/a;
c=0;
p1=p1->next;
}
k++;
printf(" %d",k);
for(int i=0;i<n;i++)
printf(" %0.5f",ptr[i].x);
printf("\n");
}while(m>=e&&k<=N);
if(k>N){
printf("用迭代法解线性方程组失败!\n");
exit(1);
}
printf(" 用Gauss-Seidel迭代法解的方程的近似解为：\n");
for(int i=0;i<n;i++)
printf(" X%d=%0.5f\n",i+1,ptr[i].x);
}
int main(){
int n,N;
float e;
struct Line *head;
printf("输入线性方程组的维数n、最大容许迭代次数N、容许误差e:\n");
printf("n=");
scanf("%d",&n);
printf("N=");
scanf("%d",&N);
printf("e=");
scanf("%f",&e);
printf("输入线性方程组的系数矩阵A及常数项Bi：\n");
for(int i=1;i<=n+1;i++){
if(i!=n+1)
printf(" X%d",i);
else printf(" B\n");
}
head=Create(n,n);
printf("\n");
head=Change(head,n);
Deal(head,e,N,n);
return 0;
}
代码运行如下：。