论文标题
二次矩阵方程的缺陷校正算法，并应用于准toeplitz矩阵
A defect-correction algorithm for quadratic matrix equations, with applications to quasi-Toeplitz matrices
论文作者
论文摘要
出现了$ a_1x^2+a_0x+a _ { - 1} = 0 $的二次矩阵方程的缺陷校正公式。通过合适的铅笔的不变子空间表达的该公式使我们能够对结构保存二倍算法（SDA）进行修改，从而使最初的近似值适用于所需的解决方案。通过选择随机矩阵作为初始近似，这种修改在收敛加速度方面的方程解决方案中提供了实质性优势。显示了在四分之一平面上求解随机步行的应用程序，其中系数$ a _ { - 1}，a_0，a_1 $是无限大小的准toeplitz矩阵。
A defect correction formula for quadratic matrix equations of the kind $A_1X^2+A_0X+A_{-1}=0$ is presented. This formula, expressed by means of an invariant subspace of a suitable pencil, allows us to introduce a modification of the Structure-preserving Doubling Algorithm (SDA), that enables refining an initial approximation to the sought solution. This modification provides substantial advantages, in terms of convergence acceleration, in the solution of equations coming from stochastic models, by choosing a stochastic matrix as the initial approximation. An application to solving random walks in the quarter plane is shown, where the coefficients $A_{-1},A_0,A_1$ are quasi-Toeplitz matrices of infinite size.
