|July 8, 2010, 18:25||
Solution of a matrix equation
Join Date: Apr 2009
Blog Entries: 1Rep Power: 6
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?
|July 10, 2010, 05:30||
Join Date: Aug 2009
Location: Wiesbaden, Germany
Posts: 241Rep Power: 7
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 ]
where DF^(-1)(v) is the inverse of DF (gradient of F).
Start with some v*
|Thread||Thread Starter||Forum||Replies||Last Post|
|Conceptual trouble--please help me understand what my matrix solution is telling me||bzz77||Main CFD Forum||0||March 25, 2010 18:31|
|OpenFOAM version 1.6 details||lakeat||OpenFOAM Running, Solving & CFD||42||August 26, 2009 22:47|
|Calculation of the Governing Equations||Mihail||CFX||5||July 25, 2008 18:29|
|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|