Single and dual wavelength exposure of photoresist
J. LaRue, C. Ting
Proceedings of SPIE 1989
This paper presents a new stochastic preconditioning approach for large sparse matrices. For the class of matrices that are rowwise and columnwise irreducibly diagonally dominant, we prove that an incomplete LDLT factorization in a symmetric case or an incomplete LDU factorization in an asymmetric case can be obtained from random walks and used as a preconditioner. It is argued that our factor matrices have better quality, i.e., better accuracy-size trade-offs, than preconditioners produced by existing incomplete factorization methods. Therefore a resulting preconditioned Krylov-subspace iterative solver requires less computation than traditional methods to solve a set of linear equations with the same error tolerance. The advantage increases for larger and denser matrices. These claims are verified by numerical tests, and we provide techniques that can potentially extend the theory to non-diagonally-dominant matrices. © 2008 Society for Industrial and Applied Mathematics.
J. LaRue, C. Ting
Proceedings of SPIE 1989
James Lee Hafner
Journal of Number Theory
A. Gupta, R. Gross, et al.
SPIE Advances in Semiconductors and Superconductors 1990
Hang-Yip Liu, Steffen Schulze, et al.
Proceedings of SPIE - The International Society for Optical Engineering