Theory, Algorithms and Models for Matrix Balancing

矩阵平衡的研究及其在数据处理中的应用 经济学中的调整将研究（1）对角标度 问题，（2）非线性网络的预处理方法 优化，和（3）二阶缩放算法。 平衡问题出现在许多不同的领域，包括经济学， 城市规划、图像处理和随机建模。PI的 建议实现缩放算法，并专门设计截断的 牛顿算法在求解问题中的应用 他们的专业知识-即一般均衡模型-在 我相信它的应用范围将超出这一特定领域。 为了解决建模问题和应用这一理论和 算法研究，他们建议作为未来的工作， 高级代数建模语言中的算法。这 将允许他们进行真实的问题的实验， 促进向广大受众传播他们的工作。支持 这项未来的研究目前正在寻求资金 除NSF之外的其他机构。

The research in matrix balancing and its application to data adjustment in economics will investigate (1) diagonal scaling problems, (2) preconditioning methods for nonlinear network optimization, and (3) second-order scaling algorithms. Balancing problems arise in many diverse fields, including economics, urban planning, image processing, and stochastic modelling. The PI's propose to implement scaling algorithms and specialize a truncated Newton algorithm for solving problems arising in the application area of their expertise-- namely, general equilibrium modelling-- in the belief that it will have application beyond that specific area. To address modeling issues and applications of this theoretical and algorithmic research they propose as future work the integration of their algorithms within high-level algebraic modelling languages. This will allow them to conduct experiments with real problems and will facilitate the dissemination of their work to a wide audience. Support for this future research is currently being sought from funding agencies other than NSF.