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SYSTEM OF LINEAR
EQUATIONS
In this chapter, we deal with several numerical schemes for solving a system of
equations
a 11 x 1 + a 12 x 2 +· · · + a 1N x N = b 1
a 21 x 1 + a 22 x 2 +· · · + a 2N x N = b 2
(2.0.1a)
.. ...... . = .
a M1 x 1 + a M2 x 2 +· · · + a MN x N = b M
which can be written in a compact form by using a matrix–vector notation as
A M×N x = b (2.0.1b)
where
a 11 a 12 · · a 1N x 1 b 1
a 21 a 22
· ·
A M×N = a 2N , x = x 2 , b = b 2
· · · · · · ·
a M1 a M2 · · a MN x N b M
We will deal with the three cases:
(i) The case where the number (M) of equations and the number (N)of
unknowns are equal (M = N) so that the coefficient matrix A M×N is
square.
Applied Numerical Methods Using MATLAB , by Yang, Cao, Chung, and Morris
Copyright 2005 John Wiley & Sons, Inc., ISBN 0-471-69833-4
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