6.5 LR method

Author: Vladislav Cale

The LR method (Rutishauser, 1958) is an iterative method used for solving eigenvalues and eigenvectors of a square matrix. A single step of LR method uses LU decomposition: a given matrix A is decomposed in product of two parts: lower diagonal matrix L containing ones on the main diagonal, and upper diagonal matrix R. Iterations can be described as follows:
A_i = L_i*R_i,
A_i+1 = R_i*L_i = L_i+1*R_i+1, i = 1,2...
Algorithm stops by exceeding specified number of iterations or if the difference between the real value of eigenvalues and the approximated values is less than a given numerical error. For further information about LU decomposition method, see LUDecomposition applet.