Approximation by Polynomials with Integral Coefficients
Le Baron O. Ferguson
xan. de 1980 · Mathematical Surveys and Monographs Libro 17 · American Mathematical Soc.
Libro electrónico
160
Páxinas
reportAs valoracións e as recensións non están verificadas Máis información
Acerca deste libro electrónico
Results in the approximation of functions by polynomials with coefficients which are integers have been appearing since that of Pal in 1914. The body of results has grown to an extent which seems to justify this book. The intention here is to make these results as accessible as possible. The book addresses essentially two questions. The first is the question of what functions can be approximated by polynomials whose coefficients are integers and the second question is how well are they approximated (Jackson type theorems). For example, a continuous function $f$ on the interval $-1,1$ can be uniformly approximated by polynomials with integral coefficients if and only if it takes on integral values at $-1,0$ and $+1$ and the quantity $f(1)+f(0)$ is divisible by $2$.The results regarding the second question are very similar to the corresponding results regarding approximation by polynomials with arbitrary coefficients. In particular, nonuniform estimates in terms of the modules of continuity of the approximated function are obtained. Aside from the intrinsic interest to the pure mathematician, there is the likelihood of important applications to other areas of mathematics; for example, in the simulation of transcendental functions on computers.In most computers, fixed point arithmetic is faster than floating point arithmetic and it may be possible to take advantage of this fact in the evaluation of integral polynomials to create more efficient simulations. Another promising area for applications of this research is in the design of digital filters. A central step in the design procedure is the approximation of a desired system function by a polynomial or rational function. Since only finitely many binary digits of accuracy actually can be realized for the coefficients of these functions in any real filter the problem amounts (to within a scale factor) to approximation by polynomials or rational functions with integral coefficients.
Valora este libro electrónico
Dános a túa opinión.
Información de lectura
Smartphones e tabletas
Instala a aplicación Google Play Libros para Android e iPad/iPhone. Sincronízase automaticamente coa túa conta e permíteche ler contido en liña ou sen conexión desde calquera lugar.
Portátiles e ordenadores de escritorio
Podes escoitar os audiolibros comprados en Google Play a través do navegador web do ordenador.
Lectores de libros electrónicos e outros dispositivos
Para ler contido en dispositivos de tinta electrónica, como os lectores de libros electrónicos Kobo, é necesario descargar un ficheiro e transferilo ao dispositivo. Sigue as instrucións detalladas do Centro de Axuda para transferir ficheiros a lectores electrónicos admitidos.
