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The first step in Givens' procedure [1] for isolating the eigenvalues of a real n × n symmetric matrix A involves reduction of A to tri-diagonal form. The usual methods for accomplishing this reduction require rapid random access to the elements of A; otherwise, for large matrices the computer time required to search (say on magnetic tape) for these elements may be much longer than the time required for actual computation. A basic reordering of operations, which avoids this difficulty and makes efficient use of auxiliary magnetic tape memory for primary storage of matrices which are too large to handle in high speed storage, is the subject of this paper) ' 2

A Modified Givens Method for the Eigenvalue Evaluation of Large Matrices