Since information gained from binary systems provides much of what we
know of the masses, luminosities, and radii of stars, eclipsing binary
models have always been and are acquiring increasing importance in
studies of stellar structure and evolution. The observational database
(photometry, spectroscopy, line profiles, polarimetry, pulse arrival
times, etc.), the degree of reality in eclipsing binary models (light
curves, radial velocities, proximity effects, X-ray binary features,
attentuating clouds, spots, etc.) and the computational power have
been increased significantly over the last 30 years.
From the mathematical point of view the computation of observables
(light curves, radial velocities, line profiles, etc.) is called the
"direct problem" while the determination of certain parameters
(masses, radii, temperatures, luminosities, orbital quantities such as
semi-major axis, eccentricity and inclination, etc.) is called the
"inverse" or "indirect problem"; usually, the inverse problem is
formulated as a least squares problem. In this talk there will be some
special focus on methods and numerical aspects related to the solution
of the nonlinear least squares problem. A special focus is on how to
analyze millions of observed light curves in surveys.
The general overview on eclipsing binaries, models, least squares
techniques and software is concluded with some results obtained in the
eclipsing binary BF Aurigae, an interesting system close to or just in
the process of mass transfer, as well as on V781 Tauri, and an outlook
into the future of eclipsing binary modeling.