Block LU decomposition

In linear algebra, a Block LU decomposition is a matrix decomposition of a block matrix into a lower block triangular matrix L and an upper block triangular matrix U. This decomposition is used in numerical analysis to reduce the complexity of the block matrix formula. In linear algebra, a Block LU decomposition is a matrix decomposition of a block matrix into a lower block triangular matrix L and an upper block triangular matrix U. This decomposition is used in numerical analysis to reduce the complexity of the block matrix formula. Consider a block matrix: where the matrix A {displaystyle {egin{matrix}Aend{matrix}}} is assumed to be non-singular, I {displaystyle {egin{matrix}Iend{matrix}}} is an identity matrix with proper dimension, and 0 {displaystyle {egin{matrix}0end{matrix}}} is a matrix whose elements are all zero.