Nonlinear numerical methods and rational approximation
著者
書誌事項
Nonlinear numerical methods and rational approximation
（Mathematics and its applications）
D. Reidel, c1988
大学図書館所蔵 全29件
注記
Includes index
"Proceedings of a conference on "Nonlinear numerical methods and Rational approximation" organised by Annie Cuyt and Luc Wuytack at the University of Antwerp (Belgium), 20-24 April 1987" -- Pref
内容説明・目次
内容説明
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; use Stein spaces. And in addition to this there are and prediction and electrical engineering can such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
目次
Pade approximation and Rational interpolation.- Integral approximants for functions of higher monodromic dimension.- Asymptotics of Hermite-Pade Polynomials and related convergence results.- Rational approximation.- On the behavior of zeros and poles of best uniform polynomial and rational approximants.- Once again: the Adamjan-Arov-Krein approximation theory.- Diagonal Pade approximants, rational Chebyshev approximants and poles of functions.- On the use of the Caratheodory-Fejer method for investigating'1/9' and similar constants.- Multidimensional and Multivariate problems.- Simultaneous rational approximation to some q-hypergeometric functions.- Minimal Pade-sense matrix approximations around s = 0 and s = ?.- (Pade)y of (Pade)x approximants of F(x,y).- Different techniques for the construction of multivariate rational interpolants.- Rational approximants of hypergeometric series in ?n.- Orthogonal polynomials and the Moment problem.- Some orthogonal systems of p+1Fp-type Laurent polynomials.- The moment problem on equipotential curves.- Difference equations, continued fractions, Jacobi matrices and orthogonal polynomials.- Multipoint Pade approximation and orthogonal rational functions.- L-Polynomials orthogonal on the unit circle.- Continued fractions.- Schur's algorithm extended and Schur continued fractions.- Some recent results in the analytic theory of continued fractions.- Best a posteriori truncation error estimates for continued fractions if (an/1) with twin element regions.- Convergence acceleration for Miller's algorithm.- Convergence acceleration.- A new approach to convergence acceleration methods.- Applications.- General T-fraction solutions to Riccati differential equations.- A simple alternative principle for rational ?-method approximation.- Evaluation of Fermi-Dirac integral.- An application of operator Pade approximants to multireggeon processes.
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