USE OF SINGULAR VALUE DECOMPOSITION FOR ANALYZING REPETITIVE MEASUREMENTS

Situations are analyzed where repetitive measurements are performed on similar physical situations. One measurement is assumed to produce one column vector of numbers. Together, the measurements produce a matrix Aij. By "similar" we mean that the columns of matrix A can be represented as linear combinations of some possible unknown basis vectors plus noise. It is shown how the singular value decomposition (SVD) of matrix A is used to analyze the contents of the matrix: the amount of noise-like experimental error is revealed, and more importantly, the presence or non-presence of any kind of distortions from the ideal situation is quantitatively estimated. The result of this analysis is summarized as the "quality number" Q of a matrix. A low Q is a warning: there is something wrong in your data. A high Q is a positive indication of the quality of the data. Experimental examples from X-ray physics are studied. It is demonstrated how SVD aids in a correction process, whereby the distortions are removed from matrix A. © 1990.