An improved algorithm for the generalized rank annihilation method

Abstract

Abstract An improved algorithm for the generalized rank annihilation method (GRAM) is presented. GRAM is a method for multicomponent calibration using two‐dimensional instruments, such as GC‐MS. In this paper an orthonormal base is first computed and used to project the calibration and unknown sample response matrices into a lower‐dimensional subspace. The resulting generalized eigenproblem is then solved using the QZ algorithm. The result of these improvements is that GRAM is computationally more stable, particularly in the case where the calibration sample contains chemical constituents not present in the unknown sample and the unknown contains constituents not present in the calibration (the most general case).