In the present paper, we propose a block variant of the extended Hessenberg process for computing approximations of matrix functions and other problems producing large-scale matrices. Applications to the computation of a matrix function such as f(A)V, where A is an nxn large sparse matrix, V is an nxp block with p<<n, and f is a function are presented. Solving shifted linear systems with multiple right hand sides are also given. Computing approximations of these matrix problems appear in many scientific and engineering applications. Different numerical experiments are provided to show the effectiveness of the proposed method for these problems.

翻译：本文提出了一种扩展Hessenberg过程的块变体，用于计算矩阵函数近似及涉及大规模矩阵的其他问题。研究展示了其在矩阵函数计算中的应用，例如f(A)V，其中A为n×n大型稀疏矩阵，V为n×p块矩阵（p<<n），f为给定函数。同时给出了求解多右端项移位线性系统的方法。此类矩阵问题的近似计算广泛出现于科学与工程应用中。通过多项数值实验验证了所提方法在这些问题上的有效性。