897 resultados para staircase approximation


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2000 Mathematics Subject Classification: 46B03

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2010 Mathematics Subject Classification: 41A25, 41A10.

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ACM Computing Classification System (1998): G.1.2.

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The deviations of some entire functions of exponential type from real-valued functions and their derivatives are estimated. As approximation metrics we use the Lp-norms and power variations on R. Theorems presented here correspond to the Ganelius and Popov results concerning the one-sided trigonometric approximation of periodic functions (see [4, 5 and 8]). Some related facts were announced in [2, 3, 6 and 7].

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We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

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AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20

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MSC 2010: 41A25, 41A35

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2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.

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2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.

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AMS classification: 41A36, 41A10, 41A25, 41Al7.

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AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

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Book review: Heidelberg, Dordrecht, London, and New York, Springer, 2010, 189 pp., £93.55 (hardcover), ISBN 978-3-642-04330-7, e-ISBN 978-3-642-04331-4

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Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

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Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

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Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.