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This project work also aims at determining the correct value of density by clearing the objects touching the borders of the image. In this project three applications are taken into account and using Matlab with image processing toolbox the count and density values are calculated for each.
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃ ə ˈ l ɛ s k i / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. This is a list of equations, by Wikipedia page under ...
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
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As another example, in n-dimensional real coordinate space without the origin (), = (+) where = + + +. which shows, for n=3 and n=5 only, is a solution to the biharmonic equation. A solution to the biharmonic equation is called a biharmonic function .
Multiple roots are highly sensitive, known to be ill-conditioned and inaccurate in numerical computation in general. A method by Zhonggang Zeng (2004), implemented as a MATLAB package, computes multiple roots and corresponding multiplicities of a polynomial accurately even if the coefficients are inexact. [3] [4] [5]
The MacCormack method is well suited for nonlinear equations (Inviscid Burgers equation, Euler equations, etc.) The order of differencing can be reversed for the time step (i.e., forward/backward followed by backward/forward). For nonlinear equations, this procedure provides the best results.