The matrix inverse and generalized inverse

Instead of using the direct singular value decomposition method, it has been decided to use a &s;quick but dirty&s; way of producing the generalized inverse, together with the undeservedly neglected method of Schultz which will then refine the initial approximate generalized inverse. Turing pointed out that one of the advantages of finding the matrix inverse when solving linear equations is that it is then possible to estimate how sensitive the x column is to small variations in the y column. The program invert applies the Schultz iterative method to calculate a generalized inverse, starting from a multiple of M . The program genfit, however, uses the main modules of matin to find fairly quickly and then produces the product M as its estimate of the generalized inverse. The central solver section of genfit is taken directly from the program matin in its original form.