Definition & Betydelse | Engelska ordet EXTREMUM

Definition av EXTREMUM

1. (matematik) extremvärde
2. (matematik) extrempunkt

Exempel på hur man kan använda EXTREMUM i en mening

• Known generically as extremum, they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function.
• For positive-semidefinite and negative-semidefinite Hessians the test is inconclusive (a critical point where the Hessian is semidefinite but not definite may be a local extremum or a saddle point).
• Bhāskara also goes deeper into the 'differential calculus' and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of 'infinitesimals'.
• Quemadmodum clepsydram non extremum stillicidium exhaurit, sed quicquid ante defluxit, sic ultima hora, qua esse desinimus, non sola mortem facit, sed sola consummat; tunc ad illam pervenimus, sed diu venimus.
• For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them.
• In the case of extremum estimators for parametric models, a certain objective function is maximized or minimized over the parameter space.
• With suitable rescaling, M-estimators are special cases of extremum estimators (in which more general functions of the observations can be used).
• There are many other multi-scale signal processing, image processing and data compression techniques, using wavelets and a variety of other kernels, that do not exploit or require the same requirements as scale space descriptions do; that is, they do not depend on a coarser scale not generating a new extremum that was not present at a finer scale (in 1D) or non-enhancement of local extrema between adjacent scale levels (in any number of dimensions).
• Papers which appeared in the Transactions of the American Mathematical Society over the next few years were: New proof of a theorem of Osgood's in the calculus of variations (1901); Proof of the sufficiency of Jacobi's condition for a permanent sign of the second variation in the so-called isoperimetric problems (1902); Weierstrass' theorem and Kneser's theorem on transversals for the most general case of an extremum of a simple definite integral (1906); and Existence proof for a field of extremals tangent to a given curve (1907).
• Successive parabolic interpolation is a technique for finding the extremum (minimum or maximum) of a continuous unimodal function by successively fitting parabolas (polynomials of degree two) to a function of one variable at three unique points or, in general, a function of n variables at 1+n(n+3)/2 points, and at each iteration replacing the "oldest" point with the extremum of the fitted parabola.
• The extremum of a binodal curve in temperature coincides with the one of the spinodal curve and is known as a critical point.
• Howbeit Mr Richard Coffyn, next heir to Sir William Coffyn, claimeth the same by his uncle's feoffment to him and to his heirs so that the law will put Mr John Basset from his entry and to compel him to take his action of form down which is much dilatory as Mr Basset knoweth albeit I intend to sue unto one writ of diem clausit extremum after the death of the said Sir William and so to find Mr Basset's title if we may come and attain any evidence, when we come home, of John Davy, to enforce the same which will cost v marks at least.
• Diem clausit extremum, a writ out of chancery to the escheator of the county upon the death of any of the king's tenants in capita, to inquire by a jury of what lands he died seised, their value and who was next heir to him.

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