The authors propose a new algorithm for the computation of eigenvalues and eigenvectors of symmetric Toeplitz matrices. The main idea behind the new algorithm is to apply the shift-and-invert technique to the well-known Lanczos method. Test results provided in the paper show a significant improvement in memory requirements compared with the classical ScaLAPACK routines. Moreover, the new method has a high degree of parallelism. The scalability of the parallel version of the new algorithm is also studied, showing scaled speedup.

The paper will be useful, especially for specialists in numerical analysis. The good performance results should motivate the selection of this method for parallel implementation in the solving process of several practical problems.