We consider symmetric positive definite preconditioners for multiple saddle-point systems of block tridiagonal form, which can be applied within the MINRES algorithm. We describe such a preconditioner for which the preconditioned matrix has only two distinct eigenvalues, 1 and -1, when the preconditioner is applied exactly. We discuss the relative merits of such an approach compared to a more widely studied block diagonal preconditioner, specify the computational work associated with applying the new preconditioner inexactly, and survey a number of theoretical results for the block diagonal case. Numerical results validate our theoretical findings.

翻译：我们认为,可以适用于MINRES算法的三对角形式块的多重马鞍点系统,具有对称性、肯定的前提条件。我们描述了这样一个先决条件,即前提条件矩阵只有两种不同的电子元值,在前提条件完全适用时只有1和1。我们讨论了这种方法的相对优点,与经过更广泛研究的区块对角前置装置相比,我们讨论了这种方法的相对优点,具体说明了与适用新的前置装置相关的计算工作,并调查了区块对角学案例的一些理论结果。数字结果证实了我们的理论结论。