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Discussion of Jacobi's method for eigenvalues
- Choose a tolerance ϵ, making it a small number, typically 10−8 or smaller.
- Setup a while test where one compares the norm of the newly computed off-diagonal matrix elements off(A)=√n∑i=1n∑j=1,j≠ia2ij>ϵ.
- Now choose the matrix elements akl so that we have those with largest value, that is |akl|=maxi≠j|aij|.
- Compute thereafter τ=(all−akk)/2akl, tanθ, cosθ and sinθ.
- Compute thereafter the similarity transformation for this set of values (k,l), obtaining the new matrix B=S(k,l,θ)TAS(k,l,θ).
- Compute the new norm of the off-diagonal matrix elements and continue till you have satisfied off(B)≤ϵ