Piecewise Linear Approximation is one of the most commonly used strategies to represent time series effectively and approximately. This approximation divides the time series into non-overlapping segments and approximates each segment with a straight line. Many suboptimal methods were proposed for this purpose. This paper proposes a new optimal approach, called OSFS, based on feasible space (FS) Liu et al. (2008)[1], that minimizes the number of segments of the approximation and guarantees the error bound using the $L\infty$-norm. On the other hand, a new performance measure combined with the OSFS method has been used to evaluate the performance of some suboptimal methods and that of the optimal method that minimizes the holistic approximation error ($L^2$-norm). The results have shown that the OSFS method is optimal and demonstrates the advantages of $L\infty$-norm over $L^2$-norm.

分段线性逼近是最有效地且近似地表示时间序列的策略之一。该近似将时间序列划分为不重叠的段，并用直线近似每个段。为此目的提出了许多次优的方法。本文提出了一种新的最优方法，称为OSFS，它基于可行空间（FS）Liu等人。（2008）[1]，它最小化了近似的分段数量，并使用$\mathrm{大号}\infty$-规范。另一方面，新的性能指标与OSFS方法相结合已用于评估某些次优方法和最优方法的性能，这些方法将整体近似误差降至最低（${\mathrm{大号}}^{\mathrm{2个}}$-规范）。结果表明，OSFS方法是最佳的，并证明了OSFS方法的优点。$\mathrm{大号}\infty$-规范 ${\mathrm{大号}}^{\mathrm{2个}}$-规范。