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.

Block LDU decompositionEdit


Block Cholesky decompositionEdit

Consider a block matrix:


where the matrix   is assumed to be non-singular,   is an identity matrix with proper dimension, and   is a matrix whose elements are all zero.

We can also rewrite the above equation using the half matrices:


where the Schur complement of   in the block matrix is defined by


and the half matrices can be calculated by means of Cholesky decomposition or LDL decomposition. The half matrices satisfy that


Thus, we have




The matrix   can be decomposed in an algebraic manner into


See alsoEdit