|
[Sponsors] |
July 8, 2010, 18:25 |
Solution of a matrix equation
|
#1 |
New Member
|
Hi Guys,
I am currently doing some analysis that requires me to solve the following matrix equation: ri = v * Ai * v' where ri is a scalar, there are many of these (>n) and they are all known. v is a row vector [v1 v2 ... vn], v' is it's transpose. Ai is an n*n matrix corresponding to the ri values, these are all known. The matrices Ai are symmetrical, real and all elements are positive. I am trying to solve this equation for the vector v. Does anyone know of a simple method to solve this, or is anyone aware of online notes that may be able to help? Many thanks, B |
|
July 10, 2010, 05:30 |
|
#2 |
Senior Member
Claus Meister
Join Date: Aug 2009
Location: Wiesbaden, Germany
Posts: 241
Rep Power: 18 |
You have a number of equations of quatratic forms. You can use Newton Approch:
f_i(v)=ri - v.Ai.v' F = [ f_1 , ... , f_n ] N(v)=v-(DF^(-1)(v))*F(v) where DF^(-1)(v) is the inverse of DF (gradient of F). Start with some v* |
|
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Calculation of the Governing Equations | Mihail | CFX | 7 | September 7, 2014 07:27 |
Conceptual trouble--please help me understand what my matrix solution is telling me | bzz77 | Main CFD Forum | 0 | March 25, 2010 17:31 |
OpenFOAM version 1.6 details | lakeat | OpenFOAM Running, Solving & CFD | 42 | August 26, 2009 22:47 |
energy equation solution | yasmeen | FLUENT | 2 | February 20, 2007 06:01 |
exact solution of burger's equation | sajar | Main CFD Forum | 9 | March 4, 2004 05:55 |