- #1
turbulent1
- 3
- 0
Solve a system of linear equations Ax=kb
A is a matrix with m*n elements,
[tex]A = \left[\stackrel{a_{11}\; \ldots \;a_{1n}}{ \vdots \ \ddots \ \vdots} {a_{m1}\cdots a_{mn} \\} \right][/tex]
[tex] \sum _{j=1} ^{n}a_{ij}=1 ,0\leq a_{ij}\leq1, 1\leq i\leq m,1\leq j \leq n , m > n[/tex]
b is a vector with m*1 elements,
[tex]0 \leq b_{i} \leq 1 \;,\; 1 \leq i \leq m [/tex],
x is the unknown vector with n*1 elements,
[tex]0 \leq x_{j} \leq 1\:,\:1 \leq j \leq n [/tex],
k is an arbitrary constant which makes x satisfy the system of equations.
find the unknown vector x.
I think it's not proper to solve the system by finding the pseudo-inverse matrix of A,
because some elements of x are than 0.
Your suggestions are welcome, thanks!
A is a matrix with m*n elements,
[tex]A = \left[\stackrel{a_{11}\; \ldots \;a_{1n}}{ \vdots \ \ddots \ \vdots} {a_{m1}\cdots a_{mn} \\} \right][/tex]
[tex] \sum _{j=1} ^{n}a_{ij}=1 ,0\leq a_{ij}\leq1, 1\leq i\leq m,1\leq j \leq n , m > n[/tex]
b is a vector with m*1 elements,
[tex]0 \leq b_{i} \leq 1 \;,\; 1 \leq i \leq m [/tex],
x is the unknown vector with n*1 elements,
[tex]0 \leq x_{j} \leq 1\:,\:1 \leq j \leq n [/tex],
k is an arbitrary constant which makes x satisfy the system of equations.
find the unknown vector x.
I think it's not proper to solve the system by finding the pseudo-inverse matrix of A,
because some elements of x are than 0.
Your suggestions are welcome, thanks!