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by Assefaw H. Gebremedhin, Fredrik Manne, Alex Pothen, Assefaw Hadish, Gebremedhin Fredrik, Manne Alex Pothen
http://www.ii.uib.no/publikasjoner/texrap/ps/2002-226.ps
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Abstract:
We revisit the role of graph coloring in modeling problems that arise in e#cient estimation of large sparse Jacobian and Hessian matrices using both finite di#erence (FD) and automatic di#erentiation (AD) techniques, in each case via direct methods. For Jacobian estimation using column partitioning, we propose a new coloring formulation based on a bipartite graph representation. This is compared with the known column intersection graph based formulation. Moreover, we analyze existing graph coloring formulations for e#cient estimation of Hessians using FD and Jacobians using AD. We identify distance-2 coloring as a unifying general problem across the di#erent cases. We also present and analyze greedy graph coloring heuristics corresponding to each case.
Citations
|
86
|
Moré, Estimation of sparse Jacobian matrices and graph coloring problems
– Coleman, J
- 1983
|
|
49
|
On the estimation of sparse Jacobian matrices
– Curtis, Powell, et al.
|
|
41
|
Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem
– McCormick
- 1983
|
|
35
|
Coloring powers of planar graphs
– Agnarsson, Halldórsson
- 2000
|
|
33
|
Approximation algorithms for channel assignment in radio networks
– Krumke, Marathe, et al.
- 1998
|
|
31
|
Estimation of sparse Hessian matrices and graph coloring problems
– Coleman, Moré
|
|
30
|
The efficient computation of sparse Jacobian matrices using automatic differentiation
– Coleman, Verma
|
|
28
|
The cyclic coloring problem and estimation of sparse Hessian amtrices
– Coleman, Cai
- 1986
|
|
26
|
On the estimation of sparse Hessian matrices
– Powell, Toint
- 1979
|
|
22
|
Computing a sparse Jacobian matrix by rows and columns
– Hossain, Steihaug
- 1998
|
|
12
|
Optimal estimation of Jacobian and Hessian matrices that arise in finite difference calculations
– Goldfarb, Toint
- 1984
|
|
8
|
Automatic Di#erentiation of Algorithms: Theory, Implementation, and Application
– Griewank, Corliss
- 1991
|
