Theory, Algorithms and Models for Matrix Balancing

矩阵平衡及其在经济学数据平差中的应用研究将研究(1)对角线标度问题，(2)非线性网络优化的预处理方法，(3)二阶标度算法。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建议实施缩放算法，并专门使用截断牛顿算法来解决其专业知识应用领域--即一般均衡建模--中出现的问题，因为他们相信，该算法将在该特定领域之外具有应用价值。为了解决建模问题和这种理论和算法研究的应用，他们建议作为未来的工作，将他们的算法集成到高级代数建模语言中。这将使他们能够用真实的问题进行实验，并将有助于将他们的工作传播给更广泛的受众。目前正在从国家科学基金会以外的资助机构寻求对这项未来研究的支持。

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.