Numerical solution of the eigenvalue problem for efficiently structured Hermitian matrices
For efficiently structured Hermitian matrices, which includes Hermitian Toeplitz plus Hankel matrices, the author introduces an \(O(n^ 2)\) FLOPS algorithm for finding specific eigenvalues, which draws onto the well- known Levinson algorithm for recursively solving equations for such matrices. The algorithm essentially uses the properties of Sturm sequences, and will work as long as the required eigenvalue is not too close to the spectrum of one of the principal minors. The paper includes numerical examples and tests to show the performance of the algorithm.
efficiently structured Hermitian matrices
scientific article; zbMATH DE number 4213319