共役勾配法による大次元スパース対称行列の固有解

抄録

This paper presents a CG method using the Sylvester law of inertia for the eigensolution of large sparse symmetric matrices and the quadratic form. The proposed method, retaining the advantages of the conjugate gradient method, permits to count the number of sign changes for given matrices by the Sylvester law of inertia, and is able to overcome the numerical difficulty caused in the case where the solution converges to the true eigenvalue. This method is particularly useful to find only small numbers of lower or upper eigenpairs in the large sparse symmetric matrices. The accuracy and stability of this method are confirmed by using several numerical examples. The numerical results give a good agreement even in the systems with multiple eigenvalues.