La obtención y proyección de tablas de mortalidad empleando curvas spline

one of the tools of numerical analysis is the use of polynomials of nth order to interpolate between n+1 points, taking cases where these polynomial functions can lead to erroneous results. an alternative is to implement polynomials of lesser order than the subsets of data. these connected polynomials are called functions of segmental interpolation (spline functions). this article introduces the tool provided by numerical analysis as a technical instrument needed to carry out all existing mathematical procedures based on algorithms to enable its simulation or calculation, in particular, the functions spline defined in ranges (by sections), with interpolation through them, giving rise to the adjustment of spline curves based on surviving an abbreviated table of mexican mortality lx series in order to disaggregate by age deployed, respecting the cavities that because of the effect of mortality in the early and following ages appear in the mexican experience. also using splines the simulations that allow obtaining future scenarios of the surviving lx series produces the mexican mortality for the years 2010-2050, projections that generate complete tables of mortality for men and women of this period, highlighting the differences between sexes and ages of their chances to survive and increments in life expectancy.