The increase of atmospheric carbon dioxide has stimulated the development
and study of global carbon models. Several models have addressed the dynamics
of the carbon cycle as a whole and attempted to estimate increases in atmospheric
concentrations of 
and ultimate effects on global climate. If the carbon cycle is modeled
as a closed system, considering the entire biosphere, and the amounts of
carbon in various compartments (such as stratosphere, troposphere, ocean
and terrestrial biota) are considered as state variables, then any variation
in fluxes between the compartments will result in perturbations of all
state values. We propose to undertake a study of this problem and analyze
the steady state system which can be written as,
matrix with the coefficients 
such that
Here, n is the number of compartments in the model and 's
are the mass/energy exchange rates between the compartments i and
j. The components of the unknown vector x will give
the amount of carbon in each compartment at the steady state. Using techniques
such as LU decomposition on equation (1)
along with the mass conservation property of the closed system, one can
solve for x. However, it is possible that the elements of
the matrix A may not have been well determined (or changing) and
corrections are needed. Under those circumstances, is there a cheaper way
of finding the new x of the corrected system making use of
the solution already in hand (i.e. without solving the problem from scratch)?
Employing the concept of pseudo-inverse, we intend to look for an answer
to this question, and provide a useful computational tool to the practitioner
for analyzing carbon models.
