On the Coding of Jacobi's Method for Computing Eigenvalues and Eigenvectors of Real Symmetric Matrices
Fernando Jose Corbató · Journal of the ACM · 1963
A technique is given which allows the coding of Jacobi's Method such that the computing time is proportional to the cube of the order of the matrix for large order matrices.The method used is one where successive rotations are chosen such that the largest magnitude off-diagonal element is the pivot; these tactics lead to a small number of rotations and a corresponding high accuracy and reduction in computing time.An algorithm for coding is offered.Jacobi's method [1,2,3,6,7] consists of performing consecutive 2-by-2 rotations of a real symmetric matrix H with elements H(km), k ~ m, where the largest magnitude off-diagonal element H(ij) is used as a "pivot."A rotation is defined as the following unitary transformation where the primes indicate the new elements.