[Users] Kranc and linear systems of equations

[Ian Hinder]

On 12 Jul 2016, at 10:23, Michael Clark <michael.clark at gatech.edu> wrote:

> Hello,
> 
> I have a system of equations for time derivatives of the form A(udot) = b, where A is a symmetric matrix, udot is a vector of time derivatives to solve for, and b is a vector of right-hand sides.
> 
> I'd like to compute the udot vector using Kranc, as the vector b involves a great deal of tensor math that I would like to use TensorTools for.
> 
> What options do I have to solve this problem?
> 
> In particular, the form of the matrix A does not change in time--only the values of its nonzero entries would vary.  If it could be factored or inverted symbolically so that the time-varying quantities could be input to it at each step, I think that would be ideal, rather than running a full matrix-inversion or factorization at every step.

Hi Michael,

A few questions:

– Is this a linear system, so that A(udot) = A . udot, or is A a general matrix-valued function of udot?

– How large is the matrix A?

– If you have a general symbolic form for A, can you compute its inverse in Mathematica, or is it too complicated?

-- 
Ian Hinder
http://members.aei.mpg.de/ianhin

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