HP 49g+, Руководство пользователя, Страница: 365 / 862

Page 11-43
The result is the augmented matrix corresponding to the system of equations:
X+Y = 0
X-Y =2
Residual errors in linear system solutions (Function RSD)
Function RSD calculates the ReSiDuals or errors in the solution of the matrix
equation
A ⋅ x
=
b
, representing a system of n linear equations in n unknowns.
We can think of solving this system as solving the matrix equation: f(
x
) =
b
-
A ⋅ x
= 0. Suppose that, through a numerical method, we produce as a first
approximation the solution
x
(0). Evaluating f(
x
(0)) =
b
-
A ⋅ x
(0) =
e ≠
0.
Thus,
e
is a vector of residuals of Function for the vector
x
=
x
(0).
To use Function RSD you need the terms
b
,
A
, and
x
(0), as arguments. The
vector returned is
e
=
b
-
A ⋅ x
(0). For example, using
A
=
[[2,-1][0,2]]
,
x
(0) =
[1.8,2.7]
, and
b
=
[1,6]
, we can find
the vector of residuals as follows:
The result is
e
=
b
-
A ⋅ x
(0) =
[ 0.1 0.6 ].
Note
: If we let the vector
∆ x
=
x
–
x
(0), represent the correction in the
values of
x
(0), we can write a new matrix equation for
∆ x
, namely
A ⋅∆ x
=
e
. Solving for
∆ x
we can find the actual solution of the original system as
x
=
x
(0) +
∆ x
.