Mathematical modeling algorithm _Geoinformatics

Mathematical modeling should have ten class algorithm 1, Monte Carlo algorithm (the algorithm also called stochastic simulation algorithms, through computer simulation to solve the problem of the algorithm, while the analog can to confirm their model is correct, is the game will use methods) 2, data fitting, parameter estimation, interpolation, and other data processing algorithms (game usually encounter a large number of data need to be addressed, and the processing of data of the key is that these algorithms typically use the Matlab as tools) 3, linear and integer programming, diverse programming, quadratic programming problems, such as planning class (modeling contest most problems belong to the optimization problems, very often, these problems can be used to describe mathematical programming, you typically use Lindo, Lingo software implementation) 4, graph theory algorithms (such algorithms can be divided into many types, including the shortest path, a network stream, bipartite graphs, algorithms, involves a graph theory problem can be solved with these methods, you need to carefully prepare) 5, dynamic programming, backtracking searches, divide and conquer algorithm, such as the computer branch and bound algorithm (these algorithms is algorithm design the more commonly-used methods, many occasions can be used to contest) 6, optimization of three non-classical algorithm: simulated annealing algorithm, neural networks, genetic algorithms (which is used to solve some of the more difficult optimization algorithms, some of the issues is helpful, but the algorithm implementation is difficult, requiring careful use) 7, grid algorithms and exhaustive method (grid arithmetic and the exhaustive search method is the most advantages of violence algorithm, in a lot of competition problems in the application, when focusing on the model itself and disdain for the algorithm, you can use this kind of violence programme, it is best to use some advanced language as a programming tool) 8, some continuous discretization (many problems are real, data can be contiguous, and the computer just recognition of a discrete data, so will their discretization for difference instead of a differential, summation instead point is very important) 9, numerical analysis algorithm (if in the game using a high-level language for programming, some commonly used in numerical analysis algorithm such as equations, matrix operations, functions, integrals, algorithm requires additional preparation library function calls) 10, image processing algorithm (the competition problem in a class of problems with the graphics, even if it has nothing to do with graphics, papers should be no lack of pictures, these graphics how to display and how to deal with is the need to resolve the problem, usually using Matlab processing) yo http://www.sciencenet.cn/m/user_content.aspx?id=382786 20 century 10 algorithm at the beginning of the century, the United States Physics (AmericanInstitute of Physics) and IEEE Computer Society (IEEE ComputerSociety) of a joint publication of the scientific and engineering computation published by Jack Dongarra, University of Tennessee and Oak Ridge National Laboratory FrancisSullivan jointly composed "century ten algorithm" article, "trying to put together in the 20th century in science and engineering development have the greatest influence over ten algorithms". Authors are suffering from a "any selection is controversial, because it is not the best algorithm", they had to use chronological order lists the ten algorithm field human wisdom bodystyling for �� gives a ranking algorithm is not ranking. Interestingly, the issue of the magazine also specifically invited these algorithms related areas of "big show" as the tenth article writing ten algorithm review article, it is awe-inspiring. The purpose of this article is to lead the readers through cursory review, together with that of the algorithm setting. 1946-Carlo method to draw a square with a square meters square, in the square inner use powder brush an irregular shape, well, can you help me calculate the area of irregular shape? Monte Carlo (MonteCarlo) way is to solve the problem of ingenious method: random to throw in the square N (N is a great natural number) soybeans, then count the number of soybean in the irregular geometric shape has an internal, for example: M a, this strange shape area will approximate the M/N, N, work out the value the more precise. Don't underestimate the number of stupid way, soya beans to national polls, small neutron mobile track, from risk analysis in financial markets, to the military exercises of sand table deduction, Monte-Carlo method for ubiquitous play behind its magical power. The Monte Carlo method is called by the United States Las Amos national laboratory of three scientists Johnvon Neumann (see clearly, the old but von Neumann comrades!), Stan Ulam and NickMetropolis joint inventions. Their very nature, the Monte Carlo method is similar to the physics of approximate method for solving the problem, it's magic lies in the fact that, for those very large-scale problems solving difficult as the dimensions of the problem (the number of arguments) increases exponentially as the levels increase, so-called "dimension of disaster" (CourseofDimensionality). To this end, the traditional methods do nothing, but you can creat a Monte Carlo method, based on the stochastic simulation of process gives the approximate results. Last eight diagrams, MonteCarlo this name come from? it is a city of Monaco to the gaming industry renowned city, gambling is in fact a deep knowledge of the probability of the door, not the? 1947 Simplex simplex method is determined by the famous "predicting the future," RAND Corporation GrorgeDantzig invention, it has become the cornerstone of linear programming subjects. The so-called linear programming, simply put, is given a set of linear (all variables are a power), constraints (such as a1 * b1 * x1 + x2 + c1 * x3 > 0), for a given objective function of extreme value. So that seems to be too wife abstract, but in reality can come in handy for example may not unusual �� for example, for a company, the production of human and material resources haveLimited ("linear constraints"), and the company's goal is to maximize profit ("objective functions take maximum"), linear and non linear abstract! as an operational research (operationresearch) part, as management science, an important tool. Which Dantzig's simplex method is similar to the linear programming problem solving an extremely effective way to shame, undergraduate second grade when I also studied a semester of operational research, now mind think of actually leaving the simplex method �� but it's not just illustrates the method is simple and intuitive? by sentence digression, wrote the Wanli fifteen years of Huang Renyu's has said that China's traditional "not from the figures on management," we used to "racking our brains," but is not based on rigorous data to make decisions, and perhaps change that traditional methods are mobilized to learn programming. 1950Krylov subspace iteration 1951 the matrix decomposition method for the early 1950 's the two algorithms are all about the matrix calculation in linear algebra, mathematical, big see readers probably see algorithm names has begun to frown at hair. Krylov subspace iteration method for solving Ax = b form, such as the equation, A is a matrix of n * n, where n is sufficiently large, immediate calculations become very difficult, and Krylov methods is subtly changes it Kxi + 1 = Kxi + b-Axi iterative solution of the form. Here's K (from author Russians NikolaiKrylov first letter of last name) is a constructed out of close to A matrix, and iterative algorithms for the beauty of forms is that it will simplify complex issues for easy calculation of stair steps. 1951 by Oak Ridge National Laboratory's AlstonHouseholder matrix decomposition method, proof of any matrix can be decomposed into triangle, diagonal, orthogonal and other special forms of matrix, the significance of the algorithm makes developing flexible matrix calculation package. 1957-optimized Fortran compiler to tell the truth, in this academic atmosphere incomparably rich list in springing a compiler (Compiler) so engineered stuff really let people have a "battle of Qin Qiong" Kuan. But another way to think of it, the door almost Fortran as scientific computing customized programming language for scientists (especially mathematicians, physicists) are simply too important to just their inseparable a Switzerland Saber, no wonder they are rushing to vote for it. You know, Fortran is the first one can be a mathematical formula into a computer program of high level language, its birth makes scientists really started using computers as tools for their research services, this is a computer application technology of a milestone in the level of contribution. On the other hand, when this help develop Fortran guy really is genius �� assembler instructions only 23500 lines completes a Fortran compiler, and the efficiency of amazing: the IBM host this project leader after decades JohnBackus, looking back at the past often laments that it generates code efficiency "was a surprise to all the developers of the imagination". It seems that as a programmer, write the program to run "came as a surprise to your own imagination," sometimes it's not necessarily a bad thing! 1959-61 computing eigenvalues of QR algorithm called, is a relevant and linear algebra algorithms studied linear algebra should remember "the eigenvalues of the matrix?" is the matrix eigenvalue of the calculation of one of the most core content, the traditional solution involves high time equation solving, when problems are large time very difficult. QR algorithm to matrix decomposition into an orthogonal matrix (what is orthogonal matrix?!, or quickly look through books!) and an upper triangular matrix product, and the previously mentioned Krylov method, which in turn is an iterative algorithm that make complex high time equation simplification for the root problem is easier to calculate stair steps, making the child used the computer for solving large-scale matrix eigenvalue becomes possible. The author of this algorithm is from the United Kingdom London J.G.F.Francis. 1962 quick sort algorithm quite a few readers may like me, see the "quick-sort algorithm" (QuickSort) this entry, the heart feels �� "this can finally find organizations." Compared to other purposes on the programmer's puzzling mathematics physics formula, quick sort algorithm is a good partner to our patrons �� the boss to let you writing a sort algorithm, if you write the quick sort is not, you are embarrassed to talk to colleagues say hello. In fact, do not implement it yourself, whether ANSI C, C + +/STL, or Java SDK, the world in almost all of the SDK can be found in its some implementation version. Quick sort algorithm earliest design by TonyHoare jazz, it's the basic idea is to be divided into two halves sort columns, the left half of the "mini 's" always on, always on the right half of the "big", and this process continues recursively continues until the entire sequence ordered. Speaking of the TonyHoare jazz, quick sort algorithm is really just he inadvertently little discovery, his contributions to computer mainly include the theory of formal methods, as well as the invention of the ALGOL60 programming language, which is obtained as a result of these achievements Turing Award in 1980. Quick sort of average time complexity only is o (Nlog (N)), compared to ordinary select sort and the bubble sort, etc., it is an historic initiative. 1965 Fast Fourier transformation to selection on our daily lives most of the algorithms, fast Fourier transform algorithm should be obvious champion �� every day when you pick up the phone, open the phone, listen to mp3, DVD, DC photographs �� it is no exaggeration to say that where digital signal processing, there is a fast Fourier transform. Fast Fourier algorithm is discrete Fourier algorithm (this is the cornerstone of digital signal processing) of a fast algorithm that has IBM Watson Research Institute of James Cooley and PrincessUniversity of Houston, its JohnTukey common time complexity is O (Nlog (N)); more important than time efficiency, fast Fourier algorithm is very easy to use hardware implementation, so it is in the field of electronic technology for a wide range of applications. 1977 integer relationship detection algorithm integer relationship detection is an old problem, its history and even can be traced back to an era of Euclid. Specifically: X1 given �� group of real numbers, X2, ..., Xn, is there not an all-zero integer a1, a2, a1 ...an, making: a 2 x 1 + x 2 + ... + n a n x = 0 this year BrighamYoung University HelamanFerguson and RodneyForcade solves this problem. As regards the significance of this algorithm, well, uh, the algorithm is applied to "simplify the quantum field theory of Feynman diagrams of computing" �� too esoteric lore la! 1987 Fast Multipole method for the calendar and turn to 1987, the year of the algorithm seems to be even more xuanao, Yale University's Leslie Greengard and VladimirRokhlin's Fast Multipole algorithm used to calculate the "through gravitational or electrostatic force interaction n accurate calculation of particle movement �� such as the star in the Galaxy, or protein interactions between atoms," Gosh, it's not that I don't understand that this world is getting faster! so-called spray washing done hero, the inventor of these algorithms has been driving cranes West lot. The twenty-first century's first five years have also been surreptitiously from our fingertips over, I wonder if next ten algorithm selection event when there again, maybe we were already hanging down old, perhaps we have not dead, just my only hope �� inside the have a Chinese name! transfers from .html http://hi.baidu.com/ak3204/blog/item/40c15a46e1c90e066b63e594