AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX

The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation to solve this problem, In this method it is necessary to follow 2n curves to handle the problem. Our method is basedon a special homotopy system of equations which consists of exactly n distinct smooth curves and connects trivial soiution to desired eigenpairs. It is important that in our method we avoidfindingexplicitlythecoefficient of the characteristic equation, as all experienced practitioners are aware of the large error that may result from the use of the approximate coefficientsof the characteristic polynomial