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Animation of Fortune's algorithm, a sweep line technique for constructing Voronoi diagrams.. In computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface to solve various problems in Euclidean space.
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. The method penalizes violations of inequality constraints using a Lagrange multiplier, which imposes a cost on violations. These added costs are used instead of the strict inequality constraints in the optimization.
Anagram: rearranging the letters of a word or phrase to produce a new word or phrase Ambigram: a word which can be read just as well mirrored or upside down; Blanagram: rearranging the letters of a word or phrase and substituting one single letter to produce a new word or phrase
As a result, the algorithm requires an upper bound on the cost that can be obtained from extending a partial solution, and this upper bound should be as small as possible. A variation of this approach called Hansen's method uses interval methods. [5] It inherently implements rectangular constraints.
For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain.
Method chaining, also known as named parameter idiom, is a common syntax for invoking multiple method calls in object-oriented programming languages. Each method returns an object, allowing the calls to be chained together in a single statement without requiring variables to store the intermediate results.