Showing papers in "The Mathematical Gazette in 1984"
TL;DR: In this article, the authors consider the problem of finding the best approximation operator for a given function, and the uniqueness of best approximations and the existence of best approximation operators.
Abstract: Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.
841 citations
TL;DR: In this paper, the authors discuss the classical axiomatic systems of Euclid and Hilbert, axiom systems for three and four dimensional absolute geometry and Pieri's system based on rigid motions.
Abstract: Discusses such topics as the classical axiomatic systems of Euclid and Hilbert, axiom systems for three and four dimensional absolute geometry and Pieri's system based on rigid motions. Models, such as Taxicab Geometry, are used to illustrate theory.
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TL;DR: The Lady or the Tiger? game as mentioned in this paper is a series of logic puzzles, ranging from the simplest problems to the most complex, where an array of imaginary characters pose questions to the players.
Abstract: \"The Lady or the Tiger?\" is a series of logic puzzles, ranging from the simplest problems to the most complex. An array of imaginary characters -- sane and insane vampires, psychiatrists, dreamers, hermits, kings, knights, knaves -- pose questions.
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TL;DR: In this article, the authors present an estimation theory for generating functions, including the limits of integral components and the expectation of prime factors, and provide hints to solve problems and solutions.
Abstract: Format.- Problems.- Estimation Theory.- Generating Functions.- Limits of Integrals.- Expectations.- Prime Factors.- Category Arguments.- Convexity.- Hints.- Solutions.