Showing papers on "Inverse trigonometric functions published in 1995"

Fast evaluation of the elementary functions in single precision

Abstract: In this paper we introduce a new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method. We assume the availability of large and fast (at least for read purposes) memory. We call this method the ATA (Add-Table lookup-Add) method. As the name implies, the hardware required for the method are adders (both two/ and multi/operand adders) and fast tables. For IEEE single precision numbers our initial estimates indicate that we can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trigonometric and inverse trigonometric functions, within the latency of two to four floating point multiplies. >

Implementation of four common functions on an LNS co-processor

Abstract: We propose a scheme for evaluating four commonly used functions namely, (1) inverse trigonometric functions, (2) trigonometric functions, (3) the exponential function, and (4) the logarithmic function with the help of a logarithmic number system (LNS) processor. A novel idea of series folding has been introduced for computing the above functions, expressed in the form of infinite series. We also show that with a suitable choice of the radix for the LNS we can evaluate exponential and logarithmic functions without using any extra hardware. >

Best trigonometric and bilinear approximations for the Besov classes of functions of many variables

Abstract: We obtain order estimates for the best trigonometric and bilinear approximations for the classesB of functions of many variables.

Algebra and Trigonometry: A Graphing Approach

Abstract: 1 Numbers, Calculations and Basic Algebra The Integers and the Rational Numbers Real Numbers and their Properties Order and Averages Exponents and their Properties Polynomials and their Factors Rational Expressions The Complex Numbers 2 Equations and Inequalities Solving Equations Algebraically Equations and Applications Displaying Equations Geometrically Graphs with Graphics Calculators Inequalities and Absolute Values Lines Some Important Quadratic Curves Linear Regression 3 Functions and Their Graphs The Function Concept Linear Functions Quadratic Functions More on Graphics Calculators Polynomial Functions Rational Functions Combinations of Functions Inverse Functions Special Functions 4 Exponential and Logarithmic Functions Exponential Functions Logarithms and Logarithmic Functions Scientific Applications Business Applications Nonlinear Regression 5 The Trigonometric Functions Right Triangle Trigonometry General Angles and Arcs The Sine and Cosine Functions Graphs of the Sine and Cosine Functions Four More Trigonometric Functions Inverse Trigonometric Functions 6 Trigonometric Identities, Equations and Laws Basic Trigonometric Identities Addition Identities More Identities Trigonometric Equations The Law of Sines The Law of Cosines Vectors 7 Systems of Equations and Inequalities Equivalent Systems of Equations Solving Systems Using Matrices The Algebra of Matrices Inverses of Matrices Determinants Systems of Inequalities 8 Analytic Geometry Parabolas Ellipses Hyperbolas Rotations Parametric Equations Polar Coordinates Polar Equations of Conics 9 Sequences, Counting and Probability Arithmetic Sequences and Sums Geometric Sequences and Sums General Sequences and Programming Mathematical Induction The Binomial Formula Counting Ordered Arrangements Counting Unordered Collections Introduction to Probablility Independence in Probability Problems Answers to Selected Problems Index

Discovering Calculus with Mathematica

Abstract: Functions and Graphs. Limits. Differentiation. Applications of the Derivative. Riemann Sums and Integration. Applications of the Integral. Logarithmic and Exponential Functions. Hyperbolic and Inverse Trigonometric Functions. Numerical Integration. Improper Integrals. Infinite Series. Polar Coordinates and Parametric Equations. Vectors and Vector Valued Functions. Partial Derivatives. Multiple Integrals and Line Integrals. Differential Equations. Appendices. Indexes.

Biologically motivated servomechanism kinematic models

Abstract: Forward and inverse kinematic models for a human like (HL) robot joint are developed and used to simulate the behavior of the joint. The forward kinematic model of the HL joint is found simply to consist of two rotational motions about fixed coordinate frames. The inverse tangent (atan2) function technique is used to develop an inverse kinematic model of the HL joint. This technique also prevents singular values from occurring in the calculations. Simulation results of the forward kinematic model are presented.

A fast algorithm for computing inverse cosine transforms for designing zero-phase FIR filters in frequency domain

Abstract: A new algorithm for computing inverse cosine transforms or for designing zero-phase FIR filters from nonuniform frequency samples is presented. The algorithm is simple, fast, recursive and can be used in 1-D or 2-D applications. Based on the three-term recursive relation of the Chebyshev polynomials, the cosine matrix is decomposed into LU products using parallel computations. Two alternative approaches-a direct and a progressive-suitable for serial computations are also derived. Given N samples, the direct version requires 2.5N/sup 2/+O(N) flops for computing the inverse cosine transforms or for calculating the filter coefficients, whereas the progressive version needs only O(5N) flops when the next N+1th sample appears. The algorithm guarantees real results and produces accurate solutions even in cases of designing high-order 1-D or 2-D FIR filters or when the interpolation matrix is ill conditioned. It can be also used in LU-factorization and can be extended to m-D filter design. >