Matrix computations (3rd ed.)
“Fe23”: a computer program for calculating the number of Fe+2 and Fe+3 ions in minerals
Computers & Geosciences
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Exchange vectors provide a convenient way to reduce the number of variables required to express a series of observed structural formulae pertaining to the same mineral. In a previous paper, an algebraic-geometric method was developed for selecting the best subset among any given set of valid exchange vectors, provided that the mineral database is large enough. In this paper, the method is further extended to include examples where the number of mineral formulae is too small. It is implemented in EVFIT, a user-friendly program which runs as script in the MATLAB® software environment. The program generates numerical results (canonical angles and sum of squares) and graphical representations (scatterplot matrices and residual error "spherical graphs") which provide the user with the necessary criteria for determining the smallest exchange vector subset that still represents the formulae with sufficient accuracy.