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Numerical analysis
Published in Alan Jeffrey, Mathematics, 2004
A number is often approximated by setting all digits to the right of the n th equal to zero, and modifying the n th digit to take account of the discarded part of the number. This process is called rounding off and it introduces an error. The convention for rounding off is that the n th digit should not be changed if the digit following it is 0, 1, 2, 3 or 4. If the digit following the n th digit is 5, 6, 7, 8 or 9 then the n th digit should be increased by one. In the event that the first discarded digit is 5, and the subsequent digits are all zeros, the last digit to be retained should only be increased by one if it is odd. A number is said to be rounded off to n significant figures when the rounding off has taken place after n digits from the first non-zero digit to occur in its representation. Sometimes the rounding off is expressed in terms of the number of decimal places that are retained.
Review of Basic Concepts
Published in Khalid Khan, Tony Lee Graham, Engineering Mathematics with Applications to Fire Engineering, 2018
In the real world, when dealing with numbers a degree of accuracy is needed. For example, if a piece of wood of a certain length was required, asking for a length of 123.732461 centimeters would not be sensible as such accurate measurements are not possible. What is more usual is some form of rounding. The method of rounding is commonly used in mathematical applications in science and engineering. It is the one generally taught in mathematics classes in high school. The method is also known as round-half-up. It works as follows:
Floating-Point Hardware
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
Rounding (or rounding-off) is the process of adjusting a numerical value so that it fits in a particular format. In general, the purpose of rounding operations is to reduce the error that arises from the loss of one or more digits. For example, the number 27,445.89 can be reduced to an integer value by truncating it to 27,445 or by rounding to 27,446. In this case the rounded value is a more accurate representation of the original number than the one obtained by chopping-off the last two digits.
Dynamic modelling of traction motor bearings in locomotive-track spatially coupled dynamics system
Published in Vehicle System Dynamics, 2022
Yuqing Liu, Zaigang Chen, Kaiyun Wang, Wanming Zhai
The secondary suspension forces between the bogie and the car body on the left and right side can be calculated as [9], The motor-gearbox suspension forces between the motor-gearbox and the bogie frame can be derived as: where Hmt and Hmw are the vertical distances between the gravity centre of the motor-gearbox and that of the bogie frame/wheelset, respectively. lm is the longitudinal distance between the gravity centre of the bogie frame and the motor-gearbox suspension position on the frame. l2 is the longitudinal distance between the gravity centre of the motor-gearbox and the motor-gearbox suspension position on the motor. The function ‘round’ is rounding the number towards the nearest integer.
A Machine Learning Approach for Quantifying the Design Error Propagation in Safety Critical Software System
Published in IETE Journal of Research, 2022
Over and above, there are different studies in the existence of bugs in critical systems. The existence of bohrbug and mandelbug in safety critical software and open source software are discussed [11,12]. Both literatures discussed on the characteristics of bohrbug and mandelbug and its mitigation. It is found that one of the solutions to mitigate is design diversity. It exposed that there is a dependency of mandelbug from interaction of the software with field elements. The study confirmed that dependencies of some bugs from environment interactions persist even after deployment [13]. Lutz et al. classified safety critical anomalies using orthogonal defect classification, aiming to improve the safety-critical software development process [14]. Benz et al. stated the software using floating-point arithmetic is prone to accuracy problems caused by rounding and catastrophic cancelation [15]. These facts aggravate bugs that are very hard to trace: the program does not necessarily crash and the results are not necessarily obviously wrong, but often subtly inaccurate. The subsequent use of these values can lead to catastrophic errors.
Fault detection filter design for a class of discrete-time impulsive switched systems with quantised signals
Published in International Journal of Systems Science, 2020
Dongsheng Chen, Cong Chen, Jian Li
Notation. In our paper, for a matrix P, and represent its transpose and inverse respectively. () denotes P is positive definiteness (negative definiteness). I and 0 denote the identity matrix and the zero matrix, respectively, with appropriate dimensions. represents the Hermitian part of the matrix P. The symbol is used to represent for convenience. The function represents rounding real number ν to the nearest integer greater than or equal to ν. denotes nonlinear systems performance gain with .