As we know, computational complexity of an algorithm is the amount of resources (time and memory) required to run it.
If I have algorithm that represents mathematical equations , how can estimate or calculate the computational complexity of these equations, the number of computation operations, and the space of memory that are used.
Related to your query, I suggest you follow https://www.thekerneltrip.com/machine/learning/computational-complexity-learning-algorithms/ and http://sharif.edu/~beigy/courses/13982/40718/Lect-12.pdf
Fatima. Your question pertains to a difficult, complex subject in computer science: analysis of algorithms, typically introduced to undergraduate computer science students, and then studied in more detail in graduate computer science classes. This is not a subject that is easily mastered by reading current, generally accepted textbooks. The answer to your question requires careful analysis and careful estimation. A standard textbook in this subject area is "Introduction to Algorithms" by cormen, leiserson, rivist, and stein, comprising 1229 pages excluding references and index.
I have a phd in computer science and would be happy to provide a simple assessment of your question if you could provide more information. Most often, a simple assessment will indicate whether the time (or space) required to complete an algorithm grows linearly with the "size" of the problem, or grows in proportion to n-squared, n-cubed, or exponentially (2 raised to the n power. ) And as a warning, a problem may have a particular pattern of growth, but an algorithm may have a more costly pattern of growth because of its implementation.
Barry Fox Thank you for your answer. Which are details you need?
If you are trying to implement a set of equations, all I need are the equations (I may have more questions after I review). If you trying to create a program that will perform some sort of data analysis, please describe the input data, the analysis that you would like to accomplish, and the output that you hope to obtain. As a simple example, if you want to determine the mean (average) value of some data, the time required to perform that work is proportional to the number of data items. If you want to sort n items into numeric order using a simple algorithm (based upon some attribute such as weight, length, or some other physical measure) the time required will be roughly n times n. (because you need to compare each item to every other item). But there are algorithms that take less time than n times n.
Barry Fox Thank you in advance for your help, I sent to you a pdf file contains the equations and describes its parameters, please check your messages box. Thank you again.
One important feature of modern computer architectures is that the amount of time necessary to perform an arithmetic operation tends to be of the same order of magnitude as the time necessary to fetch the operands from memory. As a result, on modern computers efficiency is much less immediately related to the algorithm/problem 'operation count' and much more strongly dependent on the architecture of the memory layers and on how smartly the cache memory is accessed by the specific computer implementation employed.
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