A numerical approach to the inverse Toeplitz Eigenproblem
SIAM Journal on Scientific and Statistical Computing
LAPACK's user's guide
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
The Laguerre iteration in solving the symmetric tridiagonal eigenproblem, revisited
SIAM Journal on Scientific Computing
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
Matrix computations (3rd ed.)
ScaLAPACK user's guide
Numerical Solution of the Inverse Eigenvalue Problem for Real Symmetric Toeplitz Matrices
SIAM Journal on Scientific Computing
SIAM Review
LAPACK Working Note 73: Basic Linear Algebra Communication Subprograms: Analysis and Implementation Across Multiple Parallel Architectures
Message-Passing Performance of Various Computers
Message-Passing Performance of Various Computers
A Ulm-like method for inverse eigenvalue problems
Applied Numerical Mathematics
| Hi-index | 0.00 |
In this work we describe several portable sequential and parallel algorithms for solving the inverse eigenproblem for Real Symmetric Toeplitz matrices. The algorithms are based on Newton's method (and some variations), for solving nonlinear systems. We exploit the structure and some properties of Toeplitz matrices to reduce the cost, and use Finite Difference techniques to approximate the Jacobian matrix. With this approach, the storage cost is considerably reduced, compared with parallel algorithms proposed by other authors. Furthermore, all the algorithms are efficient in computational cost terms. We have implemented the parallel algorithms using the parallel numerical linear algebra library SCALAPACK based on the MPI environment. Experimental results have been obtained using two different architectures: a shared memory multiprocessor, the SGI PowerChallenge, and a cluster of Pentium II PC's connected through a Myrinet network. The algorithms obtained show a good scalability in most cases.