Abstract The isotropic Gaussian filter is frequently used as a post-processing method for mitigating errors in Gravity Recovery and Climate Experiment (GRACE) time-variable gravity field solutions. It is known that the recurrent calculation of isotropic Gaussian filter coefficients in the spherical harmonic domain results in numerical instabilities. This issue has been recently resolved by Piretzidis & Sideris (Computers & Geosciences 133:104303) for the case of a global Gaussian filter. In this paper, we extend this work for the case of a regional Gaussian filter (i.e., a Gaussian filter with a truncated kernel). We show that instabilities also occur when the coefficients of a regional Gaussian filter are calculated using a conventional recurrence relation, and we provide methods for their proper treatment. We also briefly present some theoretical preliminaries related to recurrence relations and examine algorithms (i.e., initial value and boundary value algorithms) for their stable evaluation. Our analysis indicates that the initial value algorithms are ineffective for the calculation of regional Gaussian filter coefficients, contrary to the global Gaussian filter. The comparison of the boundary value algorithms shows that the Thomas and lower-upper (LU) decomposition algorithms are the most suitable for this case. Their main advantage is their insusceptibility to numerical limitations, such as overflow errors. The Thomas algorithm is also the most efficient in terms of computational speed.

中文翻译：

---

稳定计算各向同性高斯滤波器系数的其他方法：截断滤波器内核的情况

摘要 各向同性高斯滤波器经常被用作减轻重力恢复和气候实验 (GRACE) 时变重力场解中误差的后处理方法。众所周知，球谐域中各向同性高斯滤波器系数的循环计算会导致数值不稳定性。Piretzidis & Sideris (Computers & Geosciences 133:104303) 最近针对全局高斯滤波器解决了这个问题。在本文中，我们针对区域高斯滤波器（即具有截断内核的高斯滤波器）的情况扩展了这项工作。我们表明，当使用传统的递归关系计算区域高斯滤波器的系数时，也会出现不稳定性，并且我们提供了正确处理它们的方法。我们还简要介绍了一些与递推关系相关的理论预备知识，并检查算法（即初始值和边界值算法）的稳定评估。我们的分析表明，与全局高斯滤波器相反，初始值算法对于区域高斯滤波器系数的计算是无效的。边界值算法的比较表明，Thomas 和下上（LU）分解算法最适合这种情况。它们的主要优点是不受数值限制的影响，例如溢出错误。Thomas 算法在计算速度方面也是最有效的。我们的分析表明，与全局高斯滤波器相反，初始值算法对于区域高斯滤波器系数的计算是无效的。边界值算法的比较表明，Thomas 和下上（LU）分解算法最适合这种情况。它们的主要优点是不受数值限制的影响，例如溢出错误。Thomas 算法在计算速度方面也是最有效的。我们的分析表明，与全局高斯滤波器相反，初始值算法对于区域高斯滤波器系数的计算是无效的。边界值算法的比较表明，Thomas 和下上（LU）分解算法最适合这种情况。它们的主要优点是不受数值限制的影响，例如溢出错误。Thomas 算法在计算速度方面也是最有效的。它们的主要优点是不受数值限制的影响，例如溢出错误。Thomas 算法在计算速度方面也是最有效的。它们的主要优点是不受数值限制的影响，例如溢出错误。Thomas 算法在计算速度方面也是最有效的。