An Efficient Parallel Algorithm for the Symmetric Tridiagonal Eigenvalue Problem

An efficient parallel algorithm, which we dubbed farmzeroinNR, for the eigenvalue problem of a symmetric tridiagonal matrix has been implemented in a distributed memory multiprocessor with 112 nodes [1]. The basis of our parallel implementation is an improved version of the zeroinNR method [2]. It is consistently faster than simple bisection and produces more accurate eigenvalues than the QR method. As it happens with bisection, zeroinNR exhibits great flexibility and allows the computation of a subset of the spectrum with some prescribed accuracy. Results were carried out with matrices of different types and sizes up to 104 and show that our algorithm is efficient and scalable.

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