3 Block Diagonal Structure

1, Block-Diagonal Structure

The coefficient matrix in sets of constraints may be arranged to the matrix with several blocks, which are mutually row- and column- disjoint. It's illustrated as:

    / A1             \
    |    A2          |
A = |       A3       |
    |          A4    |
    \             A5 /

Then it can be decomposed into disjoint smaller sub-problems, which enables parallel computation to solve them dependently.

2, Double Bordered Block-Diagonal Structure (DBBB)

C = | G  L1 L2 L3 L4 L5 |

    / H  E1 E2 E3 E4 E5 \      | P  |
    | F1 D1             |      | Q1 |
A = | F2    D2          |  B = | Q2 |
    | F3       D3       |      | Q3 |
    | F4          D4    |      | Q4 |
    \ F5             D5 /      | Q5 |