A fully parallel algorithm for the symmetric eigenvalue problem
SIAM Journal on Scientific and Statistical Computing
A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem
SIAM Journal on Scientific and Statistical Computing
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Solving the symmetric tridiagonal eigenvalues problem on the hypercube
SIAM Journal on Scientific and Statistical Computing
LAPACK's user's guide
Applied numerical linear algebra
Applied numerical linear algebra
ScaLAPACK user's guide
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Parallel computation of eigenvalues and eigenvectors using occam and transputers
Parallel computation of eigenvalues and eigenvectors using occam and transputers
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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.