Abstract
We improve divide-and-conquer with multiple divisions for real symmetric tridiagonal eigenproblem proposed in [13]. The main improvements are the following two. The first is that we succeed in developing an algorithm for keeping the orthogonality among eigenvectors in double-precision floating-point number processing without a substantial increase of numerical cost. As a result, all the calculations are done without quadruple-precision floating-point number processing, which is required in [13]. The second is that we implement a deflation effect which substantially decreases numerical cost. As a result of these two improvements, we succeed in developing a program for real symmetric tridiagonal eigenproblem which is even faster than a LAPACK routine DSTEVD, while keeping a numerical accuracy comparable to DSTEVD.
