Creating an equation library (Updated 03-FEB-2017)

[Han]

(01-18-2015 08:07 PM)compsystems Wrote:  To create this eq library, is required a function that solves nonsquare systems (more unknowns than equations) to be devised an algorithm that recursively solving I think I saw one HPCalc

The plan is to use Newton's method (which is iterative). Each set of equations is transformed into functions \(\vec{F} = \langle f_1, f_2, \dotsm, f_m \rangle^T \). Applying Newton's method to solve \( \vec{F}(\vec{x}) = 0 \) would require the Jacobian. Snorre posted an example in this thread. In order to solve for \( \vec{x} \), we use SVD. This will take care of all cases, but one would have to properly interpret the solutions. SOLVESYS uses a similar scheme, but does not seem to use SVD or even LSQ for overdetermined systems.