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The implementation is based on spectral projection methods, e.g., methods based on the matrix sign function and the matrix disk function. Dune-RB: A module for the Dune library, which realizes C++ template classes for use in snapshot generation and RB offline phases for various discretizations. Apart from single-core algorithms, the package ...
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.
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 ...
That reduction function must be a computable function. In particular, we often show that a problem P is undecidable by showing that the halting problem reduces to P. The complexity classes P, NP and PSPACE are closed under (many-one, "Karp") polynomial-time reductions. The complexity classes L, NL, P, NP and PSPACE are closed under log-space ...
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 ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations N versus input size n for each function In computer science , the analysis of algorithms is the process of finding the computational complexity of algorithms —the amount of time, storage, or other resources needed to execute them.
Modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. [1] The concept of modularity is used primarily to reduce complexity by breaking a system into varying degrees of interdependence and independence across and "hide the complexity of each part behind an abstraction and interface". [2]
Many-one reductions are valuable because most well-studied complexity classes are closed under some type of many-one reducibility, including P, NP, L, NL, co-NP, PSPACE, EXP, and many others. It is known for example that the first four listed are closed up to the very weak reduction notion of polylogarithmic time projections.