readme.

To use QR to find eigenvalue of a matrix(symmetric matrix is better using QR, others may lead the result not stable.) I use the algorithm as followed:
take a matrix A, QR decompesite( use gsl function) into A=Q1*R1,
Let A2=R1*Q1, QR decomp A2 into A2=Q2*R2,
let A3=R2*Q2, repeat the processing,
Ai=Qi*Ri;A_(i+1)=Ri*Qi;
doing that many times as the difference of diag entries between i and i-1 is less than some given number(that means the 2-norm of the vector less than the number), the entries in the diag of Ai are the eigenvalues of A.

I tested this program using the matrix in the file named "matrix"
here is the result:
[kaixiany@vector3 kaixian_hw15]$ kaixian_HW15 < matrix
n====4
QR Eigenvalues of Matrix A is: 
18.565664
6.273684
2.698912
-5.538260
comparing with eval by using gsl function:
18.565664
-5.538284
2.698912
6.273708
==========================================================

the difference vector is (0,-0.000024,0,0.000024)(begin with highest)
the 2-norm of the vector is 0.000033941