  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.
