In determining an intrinsic spectrum from a measured spectrum using the Maximum Entropy Algorithm, it is hardly or even not at all practical to determine the eigenvalues of an N.times.N matrix of large dimensions (N of the order of from 10.sup.4 to 10.sup.5). According to the invention such a large matrix is subdivided into a large number of much smaller partial matrices that are located on the diagonal or trace of the large matrix. The set of eigenvalues to be determined then consists of all eigenvalues of the partial matrices which can be determined much faster. Because of the Toeplitz-like character of the partial matrices, their eigenvalues can be determined very fast by Fourier transformation of a single row of such a matrix. Using the set of eigenvalues thus obtained, the intrinsic spectrum is determined by means of a minimizing algorithm. The convergence rate of the minimizing algorithm can be highly enhanced by adding a random noise value to the variables of the minimizing process and by decreasing that noise value to zero in a number of iteration steps.
The present invention discloses a computer system and program product. A computer system including an algorithm for computing a characteristic value of a matrix comprising steps of; providing a first matrix comprising M rows and N columns (M-by-N matrix); providing second matrixes by randomly selecting rows from the first matrix, each of the second matrixes including predetermined numbers of rows smaller than the numbers of rows of the first matrix; computing the characteristic values for the second matrixes; plotting each of the characteristic values with respect to the predetermined numbers of rows; and extrapolating the plots to said number of rows of the first matrix so as to obtain a characteristic value of the first matrix.
