Block Systems

Let us consider the system in the form
 
where , and , If we represent the matrix A in the form

then

Let us find step by step the blocks and U_i:







To solve system (13), one must first solve the system

We find that





Secondly, we have to solve the system

Example 6.6.1.^* Let us solve the system of equations where

This is a block system given by relation (13) since

where and



We will express the matrix A in the form



Now we find









and

To find a solution of the system , we shall solve two systems and The system can be expressed in the form

where



and



Solving the system which can be given in the form

we obtain



Thus,