I did some number crunching and found the following:(adsbygoogle = window.adsbygoogle || []).push({});

Given n equations in n unknowns:

a*f(x) + b*g(y) = c

d*f(x) + e*g(y) = f

If there is a solution to these equations, you can use substitution to transform these equations into a set of linear equations and solve using linear algebra.

Let f(x) = u and g(y) = v

Then

a*f(x) + b*g(y) = c

d*f(x) + e*g(y) = f

which becomes

a*u + b*v = c

d*u + e*v = f

Which can be solved for u and v using linear algebra.

x and y can then be solved for by solving the corresponding equations

u = f(x), and v = g(y) thus making it possible to solve systems of non-linear equations of the form above using linear algebra.

Any thoughts?

Edwin G. Schasteen

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Using Linear Algebra to solve systems of non-linear equations

Loading...

Similar Threads for Using Linear Algebra | Date |
---|---|

A Maximization problem using Euler Lagrange | Feb 2, 2018 |

I Derivation of pi using calculus | Sep 20, 2017 |

I Linearizing vectors using Taylor Series | Aug 9, 2016 |

Solve linear equations using simplex method | Feb 6, 2012 |

Use identities to Prove linearly idenpendent | Apr 28, 2005 |

**Physics Forums - The Fusion of Science and Community**