Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems

线性方程组用于解决实际问题。 在实际问题中，方程及其解取决于通过测量物理量获得的参数以及从观察和实验中获得的数据。 关键参数值的变化将导致解决方案的变化。 该项目将制定方法，以更好地了解关键参数和解决方案之间的关系，并将新的见解应用于实际问题，如最大限度地减少火车燃料消耗，供水系统的最佳资源管理和物理系统的演变。

Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will develop methods to better understand the relationships between the key parameters and the solutions and will apply the new insights to practical problems such as the minimization of fuel consumption in trains, optimal resource management in water supply systems and the evolution of physical systems.