Numerical analysis of parametrized nonlinear equations
Numerical analysis of parametrized nonlinear equations
Parallel solution of triangular systems on distributed-memory multiprocessors
SIAM Journal on Scientific and Statistical Computing
Modified cyclic algorithms for solving triangular systems on distributed-memory multiprocessors
SIAM Journal on Scientific and Statistical Computing
Distributed orthogonal factorization
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
QR factorization of a dense matrix on a hypercube multiprocessor
SIAM Journal on Scientific and Statistical Computing
A globally convergent parallel algorithm for zeros of polynomial systems
Non-Linear Analysis
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Parallel homotopy curve tracking on a hypercube
Parallel homotopy curve tracking on a hypercube
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
A New Method for Solving Triangular Systems on Distributed Memory Message-Passing Multiprocessors
A New Method for Solving Triangular Systems on Distributed Memory Message-Passing Multiprocessors
Parallel homotopy algorithms to solve polynomial systems
ICMS'06 Proceedings of the Second international conference on Mathematical Software
| Hi-index | 0.00 |
Probability-one homotopy methods are a class of methods for solving nonlinear systems of equations that are globally convergent from an arbitrary starting point. The essence of all such algorithms is the construction of an appropriate homotopy map @r"a(@l, x) and subsequent tracking of some smooth curve @c in the zero set of the homotopy map. Tracking a homotopy curve involves finding the unit tangent vector at different points along the zero curve, which amounts to calculating the kernel of the n x (n + 1) Jacobian matrix D@r"a(@l, x). While computing the tangent vector is just one part of the curve tracking algorithm, it can require a significant percentage of the total tracking time. This note presents computational results showing the performance of several different parallel orthogonal factorization/triangular system solving algorithms for the tangent vector computation on a hypercube.