![]() ![]() Let fSmg be an in nite sequence whose limit or antilimit S can be approximated very e ciently by applying a suitable extrapolation method E0to fSmg. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems. EXTRAPOLATION METHODS AND DERIVATIVES OF LIMITS OF SEQUENCES AVRAM SIDI Abstract. ![]() The methods discussed are geared toward common problems in scientific and engineering disciplines. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. Professor Sidis work has involved the development of novel methods, their detailed mathematical analysis, design of efficient algorithms for their. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. ![]()
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