多维离散Poisson方程的矩阵―数组形式及其可解性的判定

he multidimensional discrete Poisson equation (MDPE) frequently encountered in science and engineering can be expressed, in many cases, as a brief matrix-array equation firstly defined in this paper. This new-style equation consists of a series of small matrices and can be transformed using the Kronecker sum into a familiar system of linear algebraic equations, AX=b. Then it is proved that the eigenvalues and corresponding eigenvectors of A can be obtained directly from those of these small matrices consisting in that matrix-array equation. Based on this connection, a solvability criterion for the matrix-array equation is proposed. Finally, an application of this criterion is carried out, and an inspiration from the above connection are presented and analyzed.