|July 8, 2010, 17:25||
Solution of a matrix equation
Join Date: Apr 2009
Blog Entries: 1Rep Power: 9
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, 04:30||
Join Date: Aug 2009
Location: Wiesbaden, Germany
Posts: 241Rep Power: 9
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*
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