The invention discloses a
processing method for overcoming a zero denominator condition of a matrix inversion lemma through limit operation, and a method for recursively solving an inverse matrix level by level. The method comprises the main steps of firstly, decomposing any n-order invertible matrix K into a sum of a
diagonal element matrix diag(K) and n rank-1 matrixes, defined in the specification, wherein ui is an ith column of the matrix (ki,i is set to be 0), vi is an n-dimensional
row vector (the rest are equal to 0 except vi(i) is equal to 1); secondly, according to a
recursion formula defined in the specification, performing calculation, wherein i is greater than or equal to 1 and less than or equal to n, C0 is equal to diag(K)<-1>, and Cn is equal to K<-1>; in the calculation, when an element ki,i of diag(K) is equal to 0, assuming a formula defined in the specification firstly, performing
recursion twice, and defining C2=lima->infinity(C2); and in the calculation, when the condition of 1+vi.Ci-1.ui=0 occurs, assuming a formula defined in the specification firstly, performing
recursion and defining Ci+1=lima->infinity(Ci+1). According to the
recursion method, inverse of a Hilbert matrix can be accurately solved; a Gauss-Jordan
elimination process can be realized by left multiplication of an
elimination matrix and an original matrix; and in combination with a condensable selection freedom degree of elementary matrix transformation, the
elimination matrix is used for preprocessing a finite element
stiffness matrix, so that a
condition number can be greatly reduced.