Name
Title | ||
|---|---|---|
Efficient (Partial) Determination of Derivative Matrices via Automatic Differentiation. |
Abstract | ||
|---|---|---|
In many scientific computing applications involving nonlinear systems or methods of optimization, a sequence of Jacobian or Hessian matrices is required. Automatic differentiation (AD) technology can be used to accurately determine these matrices, and it is well known that if these matrices exhibit a sparsity pattern (for all iterates), then not only can AD take advantage of this sparsity for significant efficiency gains, AD can also determine the sparsity pattern itself, with some additional work in the first iteration. Practical nonlinear systems and optimization problems often exhibit patterns beyond just "zero-nonzero." For example, some elements may be duplicates of other elements at all iterates; some elements may be constant (not necessarily zero) for all iterates. Here we show how the popular graph-coloring approach to AD can be adapted to account for these cases as well, with resulting gains in efficiency. In addition, we address the problem of determining, by AD technology, a prescribed set of the entries of the Jacobian (or Hessian, in the optimization context) matrix. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/11085061X | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
Jacobian/Hessian matrix,matrix derivative computation,automatic differentiation,partial graph coloring | Mathematical optimization,Hessian automatic differentiation,Nonlinear system,Jacobian matrix and determinant,Mathematical analysis,Matrix (mathematics),Hessian matrix,Automatic differentiation,Iterated function,Optimization problem,Mathematics | Journal |
Volume | Issue | ISSN |
35 | 3 | 1064-8275 |
Citations | PageRank | References |
1 | 0.38 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wei Xu | 1 | 9 | 2.48 |
| Thomas F. Coleman | 2 | 850 | 278.86 |