[Guide] Algorithm is an accurate and complete description of the question scheme, which is a set of clear instructions for solving problems, and the algorithm represents the policy mechanism for solving problems with the system. Weekend, today's easy conceptual summary sharing to change the world's 5 algorithms, of course, it is enough to change the world's algorithm far more than these five. For example, there is a Kalman filtering algorithm, etc., etc. will have the opportunity to organize.
Metropolis algorithm
In statistical and statistical physics, the Metropolis-Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for acquiring random sample sequences from a probability distribution that is difficult to sample. This sequence can be used for approximate distribution (eg, generating a histogram) or calculating integration (eg, a desired value). Metropolis-Hastings and other MCMC algorithms are usually used for multi-dimensional sampling, especially when dimensions are more. For one-dimensional distribution, there is usually other methods (such as adaptive rejection sampling), can be directly returned from the distribution, and these methods do not appear inherent autocorrelation samples inherent in the MCMC method.
The Metropolis algorithm is a Markov-Chain-Monte-Carlo method that generates a system state according to Boltzmann distribution. The more general Metropolis-Hastings algorithm derived from this algorithm can simulate a random variable sequence, more accurately simulated a Markov chain that is expected to be smoothly distributed, especially in the case where many random variables cannot be directly simulated. .
The algorithm is named NICHOLAS Metropolis, the latter works with Arianna W. Rosenbluth, Marshall Rosenbluth, Augusta H. Teller and Edward Teller "equation of state calculation by fast computing machine".
Why is this algorithm? The Metropolis algorithm is the most famous algorithm in Monte Carlo. Its applications include statistics, QCD, celestial physics, physical chemistry, mathematics, calculation of biological, artificial intelligence, etc., and even social sciences.
Use the Metropolis-Hastings algorithm to run the 3d Markov chain on the Rosenbrock function. The algorithm is sampled from a highly probability area, and the chain begins to mix in these areas.
Simple form
In mathematical optimization, Dantzig's single-style algorithm (or single-shaped method) is a popular algorithm for linear planning. The name of the algorithm originates from the concept of single-shaped shape, which is proposed by T. S. Motzkin. Single-shaped method (also known as simple algorithm) is a numerical optimization method for solving linear optimization problems, also known as linear programs (LP). It requires only a limited number of steps to resolve this issue, or determine its insoluble or infinity. The basic idea of simple form is proposed by George Dantzig in 1947. Since then, through a large number of improvements, they have developed into the actual most important linear optimization solution. Single pattern is pivotal method
A linear inequality system defines a multifaceted body as a serial domain. The simple algorithm starts from one starting point, moving along the edge of the polyhedron until the top of the optimal solution is reached.
Single-shaped algorithm multifisrior in 3D:
Today, the theory and algorithms of linear planning are very mature, and the application in practical problems and production and life is very wide; the birth of linear planning issues marks a new application mathematical branch - the arrival of the mathematical planning era. In the past 60 years, mathematical planning has become a mature discipline. Its theory and approach is applied to various fields such as economy, finance, military, machine learning. Many of the mathematical planning areas, many of the other important branches are established on the basis of linear planning theory and algorithms, and also use linear planning theory to solve and handle. It can be seen that the linear planning problem plays an important role in the field of mathematical planning and application mathematics. Therefore, the generation and development of the study simple formation is significant for the development of the understanding of the overall mathematical planning.
Fast Fourier algorithm
What is Fourier transform? Indicates that a function that can satisfy certain conditions is indicated as a triangular function (sinusoidal and / or cosine function) or a linear combination of their integral. In different research fields, Fourier transform has a variety of variants such as continuous Fourier transform and discrete Fourier transform. The initial Fourier analysis is proposed as a tool for analytical analysis of the heat process. Look at the approximate square wave approximation overlay process:
If a point is moving around the circumference at a constant speed, then it is a sinusoidal function from the height of the ground. The speed of the point moves corresponds to the frequency, and the radius of the circle corresponds to the amplitude.
Add a rate of round weeks
Add a few more and see:
Is it very close to the square wave?
The fast Fourier transform (FFT) is an algorithm for efficiently calculating discrete Fourier transform (DFT). It can be used to decompose digital signals into frequency components, and then analyze them. Similarly, there is a discrete Four-leaf-free fast Fourier transform (IFFT). IFFT uses the same algorithm, but has a conjugate coefficient.
The following figure shows a time domain signal to make FFT line diagrams:
Fast Fourier transform is proposed by J.W. Kuri and T.W. found in 1965. This algorithm can make the computer calculate the number of multiplication required for the discrete Fourier transform, and the more sampling points N, the more the amount of Sample of sampling is changed, the more significant saving the amount of the FFT algorithm.
James Cooley:
John Tukey:
A significant advantage of small computation, so that FFT has been widely used in signal processing technology, and combines high-speed hardware to realize real-time processing of signals. For example, the analysis and synthesis of speech signals, the multiplexing conversion of full-digit time division system and frequency division system (TDM / FDM) in the communication system, in the frequency domain to signal filtering and related analysis, by the radar, sonar Spectrum analysis of the vibration signal to increase the resolution of the target's search and tracking, etc., all to use FFT. It can be said that the emergence of FFT has played an important role in the development of digital signal processing disciplines.
Rapid sort algorithm
It is a rapid, recursive, unstable sorting algorithm, and its working principle is partial and advantage. It was the basic form of C. Anthony R. Hall (C. Antony R. Hoare in 1960, which later has been improved by many researchers. The advantage of this algorithm is that there is a very short internal cycle (this greatly increases the execution speed). It does not require additional memory (except for the additional space required to recursively call the stack).
This algorithm is applied to a large number of applications in computer science. Of course, it is also an algorithm for several algorithms of this article. This algorithm has far-reaching the modern software programming, big waves, and flows long!
QR algorithm for calculating a feature value
The QR algorithm is a numerical method for calculating all feature values and quadratic matrix feature vectors. The QR method or QR iterative method is based on QR decomposition, from John G. F. Francis and Wera Nikolajewna Kublanowskaja independently proposed in 1961-1962. Its predecessor is the LR algorithm proposed by Heinz Rutishauser (1958), which is poorly stabilized, based on LR decomposition. The iteration of the QR algorithm is often converged in the SCHUR form of the matrix. The initial process is quite complicated, so even in today's computer, it is not feasible for matrices with hundreds of thousands of rows and columns.
Delicious variants, such as Z. Bai and James Demmel 1989 multi-shift method and K. Braman, r. Byers and R. Mathias 2002's more stable variants, with actual runtime, the size is matrix Cube. The latter method is implemented in the numerical software library LAPACK, while the latter is used in numerical matrix algorithms in many computer algebraic systems (CAS).
System identification is an important part of modern control theory. Identify the structure and parameters of the system accounts for an important position in engineering and theory. The least two multiplication is an important estimation method in system parameter identification, and has been widely used in many fields and occasions.
The QR Decomposition Algorithm is one of the basic algorithms in the field of artificial intelligence, and there is this algorithm that changes the world is not exaggerated. , Read full text, original title: Talk to change the 5 largest algorithm
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