Block-iterative methods for consistent and inconsistent linear equations
Block-iterative methods for consistent and inconsistent linear equations
复制标题
DOI：
10.1007/bf01396365
复制
发表时间：
1980-03
影响因子：
2.1
通讯作者：
T. Elfving
中科院分区：
文献类型：
--
作者：
T. Elfving
We shall in this paper consider the problem of computing a generalized solution of a given linear system of equations. The matrix will be partitioned by blocks of rows or blocks of columns. The generalized inverses of the blocks are then used as data to Jacobi- and SOR-types of iterative schemes. It is shown that the methods based on partitioning by rows converge towards the minimum norm solution of a consistent linear system. The column methods converge towards a least squares solution of a given system. For the case with two blocks explicit expressions for the optimal values of the iteration parameters are obtained. Finally an application is given to the linear system that arises from reconstruction of a two-dimensional object by its one-dimensional projections.
