Quantitative information about the reservoir rock minerals is important for making technical and business decisions in hydrocarbon exploration and exploitation. Minerals are usually quantified using mineral properties available from published data and rock properties measured in the laboratory used cored samples or in the field using geochemical well logs. Despite considerable efforts by many researchers, the rapid quantification of minerals with error estimates remains a challenge. The most widely used method for rapid mineral quantification is the matrix algebra method that uses the least-squares principle. Although fast and: easy to implement, the conventional matrix algebra method is; computationally unstable leading to unrealistic values (negative or greater than one) for mineral fractions. In this paper, we present a computationally stable method that retains the speed of the conventional matrix algebra method while overcoming its limitation. The present method can be applied to both laboratory (core samples) and downhole (geochemical well logs) analyses. It is effective in handling over-determined, determined, and under-determined systems. It also handles both fixed and variable mineral properties. Unlike the conventional matrix algebra method, the present method supplements the rock and mineral properties with several constraining equations that incorporate prior information about the mineral fractions. The prior information about the mineral fractions, and the measured rock properties are weighted by the reciprocals of their respective error variances. Involving only matrix operations, the resulting equation to obtain mineral fractions is easy to implement and fast to compute. Programmed as an Excel macro or in Visual Basic, the method has been successfully implemented in our laboratory since 1993 for quantifying minerals in core samples from diverse rock formations.