对基于稀疏矩阵分解求解约束系统方法的改进

Improving the Method for Solving Constraint Systems Based on Sparse Matrix Decomposition

采用基于稀疏矩阵分解的方法 ,可以把约束系统分解成依次求解的子约束集合 ,但有时并不能顺利求解 ,其子约束集合的雅可比矩阵非满秩。本文分析了出现这种状况的几种原因 ,提出可以采用对雅可比矩阵进行下三角化求秩的方法来消除冗余约束和冗余自由度 ,然后再使用基于稀疏矩阵分解的方法进行求解。

With the method based on sparse matrix decomposition, constraint systems can be decomposed into a series of subsystems, which can be solved subsequently. But sometimes a subsystem cannot be solved, because its Jacobi matrix is not in full order. This paper analyses several reasons for this,presents a method based on calculating the order of the Jacobi matrix to eliminate redundant constraints and degrees, then the constraint system can be solved based on sparse matrix decomposition.