VEC polyRoots(double x,VEC &A,int maxiter, double eps){
int n = A.leng()-1;
double err,f,df,B_i,C_i;
VEC Z(n);
int k;
VEC B(n+1);
VEC C(n+1);
while(n>=1){
err = 1+eps;
k = 0;
while((err>=eps)&&(k<maxiter)){
B[n-1] = A[n];
C[n-1] = B[n-1];
for(int j=n-2;j>=0;j--)
B[j] = A[j+1]+x*B[j+1];
for(int j=n-3;j>=0;j--)
C[j] = B[j+1]+x*C[j+1];
B_i = A[0]+x*B[0];
C_i = B[0]+x*C[0];
f = B_i;
df = C_i;
x = x - f/df;
err = fabs(f);
k++;
}
Z[n-1] = x;
for(int j=0;j<n;j++)
A[j] = B[j];
x = Z[n-1];
n--;
}
return Z;
}
double norm2(VEC x){ //compute 2-norm
int n=x.leng();
double norm=0;
for(int i=0;i<n;i++){
norm += pow(x[i], 2);
}
norm = pow(norm, 0.5);
return norm;
}
double Lagrange(double x,VEC &XDATA,VEC &YDATA){ //use non-recursive Neville’s algorithm to calculate Lagrange Interpolation
int n=XDATA.leng(); //get the length of the vector XDATA
VEC NS(n);
for(int i=0;i<n;i++){
NS[i] = YDATA[i];
}
for(int k=1;k<n;k++){
for(int j=0;j<n-k;j++){
NS[j] = ((x-XDATA[j])*NS[j+1]-(x-XDATA[k+j])*NS[j])/(XDATA[j+k]-XDATA[j]);
}
}
return NS[0];
}
