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Engineering and Scientific Calculations
Published in David E. Clough, Steven C. Chapra, Introduction to Engineering and Scientific Computing with Python, 2023
David E. Clough, Steven C. Chapra
Calculating the absolute value of a number is easy. If the number is negative, change it to positive; otherwise, leave the number alone. The familiar symbol for the absolute value function is to surround the quantity with vertical bars, for example |x|. The absolute value function can be used in some creative ways though. For example, let’s say that you wanted to have a method of squaring a quantity yet preserving the quantity’s sign in the result. Applying this rule to -3 would yield -9, and applying it to 3 would yield 9. Consider the following formula, and you will see that it accomplishes this: x|x|
Data Types and Data Storage
Published in Julio Sanchez, Maria P. Canton, Microcontroller Programming, 2018
Julio Sanchez, Maria P. Canton
This way of designating negative numbers, called a sign-magnitude representation, corresponds to the conventional way in which we write negative and positive numbers longhand, that is, we precede the number by its sign. Sign-magnitude representation has the following characteristics: The absolute value of positive and negative numbers is the same.Positive numbers can be distinguished from negative numbers by examining the high-order bit.There are two possible representations for zero, one negative (10000000B) and one positive (00000000B).
Numeric Data in Memory
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
Notice that the left-most digit is set for a negative number and clear for a positive one. This way of designating negative numbers, called a sign-magnitude representation, corresponds to the conventional way in which we write signed numbers longhand. That is, we precede the number by its sign. Sign-magnitude representation has the following characteristics: The absolute value of positive and negative numbers is the same.Positive from negative numbers can be distinguished by examining the high-order bit. If this bit is 1, then the number is negative. Otherwise, the number is positive.There are two possible representations for zero, one negative (10000000B) and one positive (00000000B).
QR decomposition for the least squares method: theory and practice
Published in International Journal of Mathematical Education in Science and Technology, 2022
Two solutions that differ only in their signs are possible: These two solutions correspond to two values that have the same absolute value: The next c and s values correspond to the positive value and will be used further: However, direct computation of r may cause overflow or underflow of floating-point data types such as float or double in C or MATLAB because of squared and . This can be easily avoided by the simple substitutions that were probably suggested by Hammarling (1977). Let us consider the case when and the substitution is used: The sign function can be safely excluded because the same expression is present in the formulas for both c and s. And if their signs are simultaneously changed, they remain valid, see Equation (15). However, the original formulas by Hammarling (1977) contain the sign function to satisfy the optional condition.
An Improved Method for ASEP Evaluation over Fading Channels Based on Q-Function Approximation
Published in IETE Journal of Research, 2018
Aleksandar V. Markovic, Zoran H. Peric, Stefan R. Panic, Petar C. Spalevic, Bojan P. Prlincevic
Karagiannidis et al. [7] have proposed complementary error function approximation in the form ofwith parameters A and B chosen in order to minimize the integral of the absolute error in the range of interest, [0, R], i.e.where |x| denotes the absolute value. The optimal values of A = 1.98, and B = 1.135, for R = 20, are found numerically, by minimizing the integral of the absolute error.
Synchronisation in an array of spatial diffusion coupled reaction–diffusion neural networks via pinning control
Published in International Journal of Systems Science, 2018
Throughout this paper, the Lipschitz condition should be satisfied for the function fj(·), i.e. for ∀ , ∃ ξj > 0 such that where |·| denotes the absolute value.