A simple application of the homotopy method to symmetric eigenvalue problems
If A is a symmetric tridiagonal matrix, the eigenvalue problem \(Ax=\lambda x\) is approached by a homotopy which connects A to a diagonal matrix D. It is shown that, under suitable conditions, there are exactly n solution curves connecting to the desired eigenvalues and eigenvectors. It is pointed out that sparse matrix techniques can be applied to the usual path following methods.
scientific article; zbMATH DE number 3866466