AN IMPROVED METHOD FOR ALGEBRAIC ANALYSIS OF METAMORPHIC MINERAL ASSEMBLAGES

Singular value decomposition (SVD) provides a simple and straightforwa rd way of detecting univariant reactions in multicomponent mineral ass emblages. As originally developed by Fisher (1989), however, the metho d had the disadvantage that it created model mineral compositions that were not strictly stoichiometric. Model assemblages of stoichiometric minerals can be produced by rewriting the mineral composition matrix in terms of additive and exchange components and then weighting the ad ditive components more heavily than exchange components during SVD ana lysis. Prior to SVD analysis, it is generally necessary to use least-s quares methods to fit mineral analyses to stoichiometric models based on exchange and additive components; least-squares fitting of this sor t may be useful for evaluating mineral analyses even when SVD analysis is not contemplated.