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The elementary functions are constructed by composing arithmetic operations, the exponential function (), the natural logarithm (), trigonometric functions (,), and their inverses. The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's ...
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.
Analysis of algorithms, typically using concepts like time complexity, can be used to get an estimate of the running time as a function of the size of the input data. The result is normally expressed using Big O notation. This is useful for comparing algorithms, especially when a large amount of data is to be processed.
Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling , with applications in all areas of mathematical modelling .
It is possible to further reduce the program to the Karmarkar format: minimize s T x s.t. x in M ∩ K and e T x = 1. where M is a linear subspace of in R n, and the optimal objective value is 0. The method is based on the following scalar potential function: v(x) = F(x) + M ln (s T x) where F is the M-self-concordant barrier for the feasible cone.
It is impossible to count the number of steps of an algorithm on all possible inputs. As the complexity generally increases with the size of the input, the complexity is typically expressed as a function of the size n (in bits) of the input, and therefore, the complexity is a function of n. However, the complexity of an algorithm may vary ...
This problem can be solved in polynomial time, and in fact is complete for the complexity class NL. If additionally all OR operations in literals are changed to XOR operations, then the result is called exclusive-or 2-satisfiability, which is a problem complete for the complexity class SL = L.
A function problem consists of a partial function f; the informal "problem" is to compute the values of f on the inputs for which it is defined. Every function problem can be turned into a decision problem; the decision problem is just the graph of the associated function. (The graph of a function f is the set of pairs (x,y) such that f(x) = y ...