预条件的平方Smith法求解大型Sylvester矩阵方程

A preconditioned squared Smith algorithm for large Sylvester matrix equations

提出了一种预条件的平方Smith算法求解大型连续Sylvester矩阵方程,该算法利用交替方向隐式迭代(ADI)来构造预条件算子,将原方程转换为非对称Stein方程,并在Krylov子空间中应用平方Smith法迭代产生低秩逼近解。数值实验表明,与已知的Jacobi迭代法等算法相比,该算法有更好的迭代效率和收敛精度。

We propose a preconditioned squared Smith algorithm to solve large scale continuous-time Sylvester matrix equations. We firstly construct a preconditioner by using the alternating directional implicit （ADI） iteration, and transform the original equation to an equivalent non-symmetric Stein matrix equation. Then we apply the squared Smith algorithm to generate the low-rank approximation form with a Krylov subspace. Numerical experiments show that the algorithm has better iteration efficiency and convergence accuracy in comparison with the Jacobi iteration method.