Re: Large number of equations with large number of unknowns
- To: mathgroup at smc.vnet.net
- Subject: [mg27705] Re: [mg27498] Large number of equations with large number of unknowns
- From: "Eckhard Hennig" <Eckhard.Hennig at eplus-online.de>
- Date: Mon, 12 Mar 2001 02:09:48 -0500 (EST)
- References: <984v2g$56l@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Mark Harder" <harderm at ucs.orst.edu> schrieb im Newsbeitrag news:984v2g$56l at smc.vnet.net... > Derek, > You say you have linearly independent equations that you are trying to > solve for the "values" of the variables with Solve[]. However, I always > thought Solve was for solving nonlinear equations , Polynomial systems, and > mixtures. Mark, this is not the whole truth. Here are two points from the documentation of Solve: * Solve deals primarily with linear and polynomial equations. * Solve uses special efficient techniques for handling sparse systems of linear equations with approximate numerical coefficients. And besides, even if Solve was designed for nonlinear systems, it would solve linear systems just as well. For example, Newton's method solves linear equations in one step, and Groebner basis methods also work for linear systems (in fact, these methods reduce to simple Gaussian elimination when applied to linear equations). Best regards, -- Eckhard