Five new algorithms were proposed in order to optimize well conditioning of structural matrices. Along with decreasing the size and duration of analyses, minimizing analytical errors is a critical factor in the optimal computer analysis of skeletal structures. Appropriate matrices with a greater number of zeros (sparse), a well structure, and a well condition are advantageous for this objective. As a result, a problem of optimization with various goals will be addressed. This study seeks to minimize analytical errors such as rounding errors in skeletal structural flexibility matrixes via the use of more consistent and appropriate mathematical methods. These errors become more pronounced in particular designs with ill-suited flexibility matrixes; structures with varying stiffness are a frequent example of this. Due to the usage of weak elements, the flexibility matrix has a large number of non-diagonal terms, resulting in analytical errors. In numerical analysis, the ill-condition of a matrix may be resolved by moving or substituting rows; this study examined the definition and execution of these modifications prior to creating the flexibility matrix. Simple topological and algebraic features have been mostly utilized in this study to find fundamental cycle bases with particular characteristics. In conclusion, appropriately conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

翻译：提议了五个新的算法,以优化结构矩阵的优化。除了缩小分析的规模和持续时间外,尽量减少分析错误是最佳计算机分析骨骼结构的一个关键因素。适当的矩阵,其数量为零(粗糙)、结构良好和条件良好,对这一目标有利。因此,将解决与各项目标优化的问题。本研究报告力求通过使用更加一致和适当的数学方法,尽量减少骨骼结构灵活性矩阵圆形错误等分析错误。这些错误在特别设计中更加明显,使用不合适的弹性矩阵;结构不均是这方面的一个常见例子。由于使用薄弱的元素,灵活性矩阵有许多非直径术语,导致分析错误。在数字分析中,矩阵的缺陷可能通过移动或替换行来解决;本研究报告研究了这些修改的定义和执行,然后采用了灵活性矩阵。本研究报告主要利用了简单的表层和代数特征,以找到具有特定特点的基本周期基础。结论是,因此,降低了有适当条件的矩阵。因此,减少了分析错误。