HP 50G, User Manual

Page: 371 / 887

Page 11-44
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
Δ
x = x – x (0), represent the correction in the
values of x (0), we can write a new matrix equation for
Δ
x , namely A
⋅Δ
x = e .
Solving for
Δ
x we can find the actual solution of the original system as x =
x (0) +
Δ
x .