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Value Engineering of Requirements
Published in Phillip A. Laplante, Mohamad H. Kassab, Requirements Engineering for Software and Systems, 2022
Phillip A. Laplante, Mohamad H. Kassab
On the other hand, algorithmic complexity reflects the complexity of the algorithm used to solve the problem. A key distinction between computational complexity theory and analysis of the algorithm is that the latter is devoted to analyzing the number of resources needed by a particular algorithm to solve a concrete problem, whereas the former asks a more general question. Namely, it targets classifying problems that can, or cannot, be solved with appropriately restricted resources. A mathematical notation called big-O notation is used to define an order relation on functions. The big-O form of a function is derived by finding the dominating term f(n). Big-O notation captures the asymptotic behavior of the function. Using this notation, the efficiency of algorithm A is O(f(n)), where, for input size n, algorithm A required at most O(f(n)) operations in the worst case.
Functions and their curves
Published in John Bird, Bird's Higher Engineering Mathematics, 2021
An asymptote to a curve is defined as a straight line to which the curve approaches as the distance from the origin increases. Alternatively, an asymptote can be considered as a tangent to the curve at infinity.
Algorithmic Improvements to MCNP5 for High-Resolution Fusion Neutronics Analyses
Published in Fusion Science and Technology, 2018
Scott W. Mosher, Stephen C. Wilson
The asymptotic complexity13 of several algorithms implemented in MCNP5 is considered. Asymptotic notation, commonly referred to as “Big-O notation,” is used to describe the limiting performance behavior of an algorithm as the amount of input to be processed or searched becomes large. For example, the run time or number of iterations of an O(n) algorithm increases linearly with the size of the input n. In some cases, algorithms operate on multiple sets of inputs simultaneously. For simplicity, a formally O(m⋅n) algorithm will be described as having O(n2) performance if the sizes of both input sets m and n tend to become large in highly detailed geometry models. The actual performance of the various algorithms in specific test cases is evaluated in Sec. III.