Showing papers on "Inverse trigonometric functions published in 1989"
TL;DR: In this article, Stechkin and Telyakovskii give an approximation of differentiable functions by trigonometric polynomials in the L metric using the Fourier series.
Abstract: their Fourier series," Mat. Zametki, ~, 291-300 (1968). 13. S. B. Stechkin, "An estimation of the remainders of the Fourier series of differentiable functions," Tr. Mat. Inst. Akad. Nauk SSSR, 145, 126-151 (1980). 14. A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987). 15. H. B. Dwight, Tables of Integrables and Other Mathematical Data, 4th edn., The Macmillan Company, New York (1961). 16. S. M. Nikol'skii, "Approximation of functions in the mean by trigonometric polynomials," Izv. Akad. Nauk SSSR, Ser. Mat., i0, 207-256 (1946). 17. N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965). 18. S. B. Stechkin and S. A. Telyakovskii, "On approximation of differentiable functions by trigonometric polynomials in the L metric," Tr. Mat. Inst. Akad. Nauk SSSR, 88, 20-29 (1967).
6 citations
5 citations
14 May 1989
TL;DR: It is demonstrated that inverse kinematic solutions can be described by two-dimensional vector rotations and arc tangent operations and that these operations can be efficiently computed by the coordinate rotation digital computer (CORDIC) algorithms.
Abstract: The authors present an LSI (large-scale integrated) circuit for high-speed inverse kinematics computation. They demonstrate that inverse kinematic solutions can be described by two-dimensional vector rotations and arc tangent operations and that these operations can be efficiently computed by the coordinate rotation digital computer (CORDIC) algorithms. The chip is fabricated using 1.5- mu m CMOS gate array technology, and the design of the arithmetic unit on the chip is based on the CORDIC algorithms. Pipelining is fully used in the processor to enhance the operating ration up to 100%. The resulting compact inverse kinematics processor is composed of the above chip and a few memory chips for program and data. The processor can be used for various kinds of manipulators. >
5 citations
TL;DR: This paper describes the problem of selection of an appropriate branch of multiple-valued functions and discusses how to select FORTRAN functions "ATan" and "ATAN2', and how to evaluate the formula [arctan [EQUATION].
Abstract: This paper describes the problem of selection of an appropriate branch of multiple-valued functions. Real-valued arctangent function over real number filed is considered as an example. It is discussed how to select FORTRAN functions "ATAN" and "ATAN2', and how to evaluate the formula [arctan [EQUATION]. Minute post-conditioning is required for transferring the result of computer algebra to numerical computation.
3 citations
2 citations
1 citations
01 Jan 1989
TL;DR: It is demonstrated that inverse kinematic solutions can be described by the 2-dimensional vector rotations and the arctangent operations, and these operations can be efficiently computed by the Coordinate Rotation DIgital Computer( CORDIC ) algorithms.
Abstract: This paper presents an LSI for high-speed inverse kinematics computation. It is demonstrated that inverse kinematic solutions can be described by the 2-dimensional vector rotations and the arctangent operations, and these operations can be efficiently computed by the Coordinate Rotation DIgital Computer( CORDIC ) algorithms. The chip is fabricated with the 1.5-pm CMOS gate array, and the design of the arithmetic unit on the chip is based on the CORDIC algorithms. Pipelining is fully used in the processor to enhance the operating ratio up to 100%. The inverse kinematics processor is compactly composed of the fabricated chip and a few memory chips for program and data. The processor performs the inverse kinematics computation according to the program, and the processor can be universally used for various kinds of manipulators.