Algorithmic Aspects of Vertex Elimination on Graphs
- D. Rose, R. Tarjan, G. S. Lueker
- MathematicsSIAM journal on computing (Print)
- 1 June 1976
A graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric positive definite systems of linear equations is considered, and it is conjecture that the problem of finding a minimum ordering is NP-complete.
Generalized nested dissection
It is shown that sparse Gaussian elimination is efficient for any class of graphs which have good separator, and conversely that graphs without good separators are not amenable to sparse GaRussian elimination.
Triangulated graphs and the elimination process
- D. Rose
- Mathematics
- 1 December 1970
Some errors estimates for the box method
We define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane. Our estimates show the error to be comparable to a standard Galerkin finite…
Algorithmic aspects of vertex elimination on directed graphs.
We consider a graph-theoretic elimination process which is related to performing Gaussian elimination on sparse systems of linear eauations. We give efficient algorithms to: (1) calculate the fill-in…
A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS
- D. Rose
- Computer Science
- 1972
Global approximate Newton methods
SummaryWe derive a class of globally and quadratically converging algorithms for a system of nonlinear equations,g(u)=0, whereg is a sufficiently smooth homeomorphism. Particular attention is…
Transient simulation of silicon devices and circuits
- R. Bank, W. M. Coughran, W. Fichtner, E. Grosse, D. Rose, R. K. Smith
- Computer ScienceIEEE Transactions on Electron Devices
- 1 October 1985
An overview of the physical principles and numerical methods used to solve the coupled system of non-linear partial differential equations that model the transient behavior of silicon VLSI device structures and a simple data structure for nonsymmetric matrices with symmetric nonzero structures is presented.
Numerical methods for semiconductor device simulation
- R. Bank, D. Rose, W. Fichtner
- Computer ScienceIEEE Transactions on Electron Devices
- 1 September 1983
This paper describes the numerical techniques used to solve the coupled system of nonlinear partial differential equations which model semiconductor devices, and the efficient solution of the resulting nonlinear and linear algebraic equations.
Algorithmic aspects of vertex elimination
It is claimed that the minimum ordering problem for directed graphs is NP-complete, and conjecture that it is also NP- complete for undirected graphs.
...
...