APPROXIMATING DOMINANT EIGENVALUES AND EIGENVECTORS OF THE LOCAL FORECAST ERROR COVARIANCE-MATRIX

Examining the dominant eigenvectors of a forecast error covariance mat rix for Western Europe during a 607-day period, shows that these daily changing vectors remain in a low-dimensional space. The first few dom inant eigenvectors of each day can almost completely be described by a fixed basis consisting of a relatively small number of elements. A si mple method is presented that utilizes this property to determine the daily dominant eigenvectors and eigenvalues of the covariance matrix i n an efficient manner. Results are given for a 2-day forecast period, but apply also for a forecast period of 3 days. Use of the method, ins tead of the Lanczos algorithm, in approximating the seven largest eige nvalues within a 1% accuracy level, resulted in a 30% reduction of the computational costs.