| A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information.;In the present work an essentially different approach to resolve this problem is developed.;First, the well-known identity which determines the jumps of a function of bounded variation by its differentiated Fourier series is extended to larger classes of functions, such as ;Next, a method based on these identities is developed. The method enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. The accuracy of approximations is studied and asymptotic expansions for the approximation of the location of the discontinuity and the magnitude of the jump of a 2;The description of a programmable algorithm for the approximations of the discontinuities and the associated jumps of a bounded function is given and some numerical examples are presented.;In conclusion, our results are compared with those of other researchers and weak and strong points of our method are discussed.;The results of the present dissertation are either published (24, 26), submitted for publication (25), or to be submitted for publication (27). |
