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Direct Method (sculpture)
Direct method may refer to * Direct method (education) for learning a foreign language * Direct method (computational mathematics) as opposed to iterative method *Direct methods (crystallography) for estimating the phases of the Fourier transform of the scattering density from the corresponding magnitudes *Direct method in calculus of variations In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Stanisław Zaremba and David Hilbert around 1900. The method relie ... for constructing a proof of the existence of a minimizer for a given functional * Direct method (accounting) as opposed to indirect method for calculating cash flows {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Method (computational Mathematics)
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''i''-th approximation (called an "iterate") is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of an iterative method or a method of successive approximation. An iterative method is called '' convergent'' if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution (for example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Methods (crystallography)
In crystallography, direct methods are a family of methods for estimating the phases of the Fourier transform of the scattering density from the corresponding magnitudes. The methods generally exploit constraints or statistical correlations between the phases of different Fourier components that result from the fact that the scattering density must be a positive real number. In two dimensions, it is relatively easy to solve the phase problem directly, but not so in three dimensions. The key step was taken by Hauptman and Karle, who developed a practical method to employ the Sayre equation for which they were awarded the 1985 Nobel prize in Chemistry. The Nobel Prize citation was "for their outstanding achievements in the development of direct methods for the determination of crystal structures." At present, direct methods are the preferred method for phasing crystals of small molecules having up to 1000 atoms in the asymmetric unit. However, they are generally not feasible by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Method In Calculus Of Variations
In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by StanisÅ‚aw Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of a solution, direct methods may be used to compute the solution to desired accuracy. The method The calculus of variations deals with functionals J:V \to \bar, where V is some function space and \bar = \mathbb \cup \ . The main interest of the subject is to find ''minimizers'' for such functionals, that is, functions v \in V such that J(v) \leq J(u) for all u \in V . The standard tool for obtaining necessary conditions for a function to be a minimizer is the Euler–Lagrange equation. But seeking a minimizer amongst functions satisfying these may lead to false conclusions if the existence of a minimizer is not established beforeha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |