Abstract
The iterative proportional scaling algorithm is generalized to find real positive solutions to polynomial systems of the form: \( \sum\nolimits_{j = 1}^m {a_{sj} p_j = c_s ,s = 1,...,n,} \) where \( p_j = \pi _j \prod\nolimits_{s = 1}^n {x_s^{a_{sj} } } \) with a sj ∈ ℝ and π j , c s ∈ ℝ>0. These systems arise in the study of reversible self-assembly systems and reversible chemical reaction networks. Geometric properties of the systems are explored to extend the iterative proportional scaling algorithm. They are also applied to improve the convergent rate of the iterative proportional scaling algorithm when dealing with ill-conditioned systems. Reduction to convex optimization is discussed. Computational results are also presented.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Huang, MD., Luo, Q. (2007). On the Extended Iterative Proportional Scaling Algorithm. In: Wang, D., Zhi, L. (eds) Symbolic-Numeric Computation. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7984-1_18
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DOI: https://doi.org/10.1007/978-3-7643-7984-1_18
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7983-4
Online ISBN: 978-3-7643-7984-1
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