Topic

# Division (mathematics)

About: Division (mathematics) is a(n) research topic. Over the lifetime, 12717 publication(s) have been published within this topic receiving 87814 citation(s).

##### Papers published on a yearly basis

##### Papers

More filters

•

[...]

01 May 1981

TL;DR: This book will be most useful to applied mathematicians, communication engineers, signal processors, statisticians, and time series researchers, both applied and theoretical.

Abstract: This book will be most useful to applied mathematicians, communication engineers, signal processors, statisticians, and time series researchers, both applied and theoretical. Readers should have some background in complex function theory and matrix algebra and should have successfully completed the equivalent of an upper division course in statistics.

3,230 citations

••

[...]

TL;DR: An algorithm is given for computer control of a digital plotter that may be programmed without multiplication or division instructions and is efficient with respect to speed of execution and memory utilization.

Abstract: An algorithm is given for computer control of a digital plotter.
The algorithm may be programmed without multiplication or division instructions and is efficient with respect to speed of execution and memory utilization.

2,124 citations

•

[...]

TL;DR: The principles of the algorithms available for performing arithmetic operations in digital computers, described independently of specific implementation technology and within the same framework, are explained.

Abstract: This text explains the fundamental principles of algorithms available for performing arithmetic operations on digital computers. These include basic arithmetic operations like addition, subtraction, multiplication, and division in fixed-point and floating-point number systems as well as more complex operations such as square root extraction and evaluation of exponential, logarithmic, and trigonometric functions. The algorithms described are independent of the particular technology employed for their implementation.

1,148 citations

••

[...]

TL;DR: In this article, the behaviour of the limits surface defined by a recursive division construction can be analyzed in terms of the eigenvalues of a set of matrices, and suggestions for the further improvement of the method are made.

Abstract: The behaviour of the limits surface defined by a recursive division construction can be analysed in terms of the eigenvalues of a set of matrices. This analysis predicts effects actually observed, and leads to suggestions for the further improvement of the method.

931 citations

••

[...]

TL;DR: It is shown that arithmetic expressions with n ≥ 1 variables and constants; operations of addition, multiplication, and division; and any depth of parenthesis nesting can be evaluated in time 4 log 2 + 10(n - 1) using processors which can independently perform arithmetic operations in unit time.

Abstract: It is shown that arithmetic expressions with n ≥ 1 variables and constants; operations of addition, multiplication, and division; and any depth of parenthesis nesting can be evaluated in time 4 log2n + 10(n - 1)/p using p ≥ 1 processors which can independently perform arithmetic operations in unit time. This bound is within a constant factor of the best possible. A sharper result is given for expressions without the division operation, and the question of numerical stability is discussed.

839 citations