The masked projection techniques are popular in the area of non-linear model reduction. Quantifying and minimizing the error in model reduction, particularly from masked projections, is important. The exact error expressions are often infeasible. This leads to the use of error-bound expressions in the literature. In this paper, we derive two generalized error bounds using cosine-sine decomposition for uniquely determined masked projection techniques. Generally, the masked projection technique is employed to efficiently approximate non-linear functions in the model reduction of dynamical systems. The discrete empirical interpolation method (DEIM) is also a masked projection technique; therefore, the proposed error bounds apply to DEIM projection errors. Furthermore, the proposed error bounds are shown tighter than those currently available in the literature.

翻译：掩蔽投影技术在非线性模型降阶领域应用广泛。量化并最小化模型降阶中的误差，特别是掩蔽投影带来的误差，具有重要意义。精确的误差表达式通常难以获得，这导致文献中常采用误差界表达式。本文针对唯一确定的掩蔽投影技术，利用余弦-正弦分解推导出两个广义误差界。一般而言，掩蔽投影技术用于在动力系统模型降阶中高效逼近非线性函数。离散经验插值方法（DEIM）同样是一种掩蔽投影技术，因此所提出的误差界适用于DEIM投影误差。此外，研究证明所提出的误差界比现有文献中的误差界更为紧致。