An application of preconditioned conjugate gradients to relative placement in chip design
Please always quote using this URN: urn:nbn:de:bvb:20-opus-31996
- In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-largescale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. NumericalIn distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-largescale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.…
Author: | Christian Kredler, Christian Zillober, Frank Johannes, Georg Sigl |
---|---|
URN: | urn:nbn:de:bvb:20-opus-31996 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Year of Completion: | 1993 |
Source: | In: International Journal for Numerical Methods in Engineering (1993) 36, 255-271. |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Release Date: | 2008/12/18 |