/*	prog3a.c -- Find the Eigenvalue of Largest Absolute Value
	Written Sep 28, 2002 by Eric Olson for Mathematics 483

	For more information see Section 1.7 in Numerical Analysis
	for Applied Mathematics, Science and Engineering by Donald
	Greenspan and Vincenzo Casulli. */

#include <stdio.h>
#include <math.h>

#define N 45

double A[N][N];
double w[N],y[N];

main(){
	double lambda,lambda_old;
	int i,j,k,n,c;
	puts("prog3a.c -- Find the Eigenvalue of Largest Absolute Value\n");

	for(n=1;n<=N;n++){
		lambda=1000.0;
		for(i=0;i<n;i++) for(j=0;j<n;j++) {
			if(i==j) A[i][j]=-2.0;
			else if(i==j+1 || i+1==j) A[i][j]=1.0;
			else A[i][j]=0.0;
		}
		y[0]=1.0; for(i=1;i<n;i++) y[i]=0.0;
	
		for(c=k=0;lambda_old!=lambda;c++){
			for(i=0;i<n;i++) {
				double s=0.0;
				for(j=0;j<n;j++){
					s+=A[i][j]*y[j];
				}
				w[i]=s;
			}
			lambda_old=lambda;
			lambda=w[k]/y[k];
		
			for(k=0,i=1;i<n;i++){
				if(fabs(w[k])<fabs(w[i])) k=i;
			}
			for(i=0;i<n;i++) y[i]=w[i]/w[k];
			if(c>30000){
				printf("Didn't converge: ");
				lambda_old=lambda;
			}
		}
		printf("n=%d lambda=%g rho(A)=%g\n",n,lambda,fabs(lambda));
	}
	return 0;
}