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Showing papers on "Inverse trigonometric functions published in 1986"


Journal ArticleDOI
TL;DR: In this article, the authors investigated the approximation of functions of several variables with a bounded mixed derivative or difference, and obtained embedding theorems and estimates for the best approximations by trigonometric polynomials to functions in these classes.
Abstract: The author investigates questions of the approximation of functions of several variables with a bounded mixed derivative or difference. He finds the orders of the Kolmogorov widths and of other widths of these classes. He obtains embedding theorems and estimates for the best approximations by trigonometric polynomials to functions in these classes. Bibliography: 33 titles.

20 citations


Proceedings ArticleDOI
04 Apr 1986
TL;DR: The algorithms thus derived have a simple structure and exhibit uniform convergence inside an adjustable, precisely defined, domain and an efficient way of extending the domain of convergence for the hyperbolic functions.
Abstract: In 1971, J.S. Walther generalized and unified J.E. Volder's coordinate rotation (CORDIC) algorithms. Using Walther's algorithms a few commonly used functions such as divide, multiply-and-accumulate, arctan, plane rotation, arctanh, hyperbolic rotation can be implemented on the same simple hardware (shifters and adders, elementary controller) and computed in approximately the same time. Can other useful functions be computed on the same hardware by further generalizing these algorithms? Our positive answer lies in a deeper understanding of Walther's unification: the key to the CORDIC algorithms is that all of them effect the multiplication of a vector by the exponential of a 2 X 2 matrix. The importance of this observation is readily demonstrated as it easily yields the convergence conditions for the CORDIC algorithms and an efficient way of extending the domain of convergence for the hyperbolic functions. A correspondence may be established between elementary functions such as square-root, √(x2+y) , inverse square-root or cubic root and exponentials of simple matrices. Whenever such a correspondence is found, a CORDIC-like algorithm for computing the function can be synthesized in a very straightforward manner. The algorithms thus derived have a simple structure and exhibit uniform convergence inside an adjustable, precisely defined, domain.

14 citations


Proceedings ArticleDOI
01 Apr 1986
TL;DR: A new algorithm for the inverse Cosine transform (IDCT) is developed which falls within the unified architecture if the authors allow ourselves the luxury of double length processing.
Abstract: A common architecture, which is based on the Cooley-Tukey[1] algorithm, is developed for the Fourier, Hadamard, and forward and inverse Cosine transforms. The theory to implement the first three transforms in this architecture is well known. However, the existing algorithms for the inverse Cosine transform (IDCT) would disqualify it from the unified architecture and this led us to develop a new IDCT algorithm which falls within the unified architecture if we allow ourselves the luxury of double length processing. Details of the unified architecture and the new algorithm for the IDCT will be given in this paper.

5 citations