为求解奇异线性鞍点问题，应用正定对称块对角预条件子，对奇异鞍点线性系统（1）进行预条件处理，讨论了块对角预条件奇异线性系统矩阵的特征值分布，得到预条件系统矩阵的非零特征值的分布范围及特征值1和0的代数重数。发现此预条件子满足恰当分裂，进一步得到了预条件GMRES算法和预条件TFQMR算法求解此块对角预条件奇异线性系统的收敛性。数值实验表明：预条件GMRES算法和预条件TFQMR算法比直接使用GMRES算法和TFQMR算法有明显的优越性。

In order to solve the singular linear saddle point problem, the positive definite symmetric block diagonal preconditioner is used for the singular saddle point linear system (1). The eigenvalue distribution of the matrix of the block diagonal preconditioned singular linear system is discussed. The distribution range of the nonzero eigenvalues of the preconditioned system matrix and the algebraic multiplicity of the eigenvalues 1 and 0 are obtained. We find that the preconditioner satisfies the proper splitting, and further obtain the convergence of the preconditioned GMRES algorithm and the preconditioned TFQMR algorithm for solving this block diagonal preconditioned singular linear system. Numerical experiments show that the preconditioned GMRES algorithm and the preconditioned TFQMR algorithm have obvious advantages over the GMRES algorithm and TFQMR algorithm without preconditioning.