Numerical Equation Solving
The function for solving equations numerically, FindRoot, now supports array and vector
variables. Additionally included are new and improved algorithms that
lead to speed increases and better handling of large-scale problems on
computers with limited memory.
Example: Solving Matrix Equations
Here is an example of solving a matrix equation--in this case the
continuous-time algebraic Riccati equation  .
Suppose we have the following system and constraints. We can
use FindRoot to find a matrix root to the equation.
![A = ([row 1] 0 1 [row 2] 0 0) ; B = ([row 1] 0 [row 2] 1) ;](images/findroot_2.gif "A = ([row 1] 0 1 [row 2] 0 0) ; B = ([row 1] 0 [row 2] 1) ;")
![Q = ([row 1] 1 0 [row 2] 0 1 ); R = (1) ;](images/findroot_3.gif "Q = ([row 1] 1 0 [row 2] 0 1 ); R = (1) ;")
![FindRoot[P . A + A^T . P - P . B . R^(-1) . B^T . P [LongEqual]
-Q, {P, ([row 1] 10 2 [row 2] 2 10) } ]](images/findroot_4.gif "FindRoot[P . A + A^T . P - P . B . R^(-1) . B^T . P [LongEqual]
-Q, {P, ([row 1] 10 2 [row 2] 2 10) } ]")
![{P -> ([row 1] 1.73205 1. [row 2] 1. 1.73205) }](images/findroot_5.gif "{P -> ([row 1] 1.73205 1. [row 2] 1. 1.73205) }")
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