Identification example: least squares method to fit the standard equation of a circle The following uses the equation of a fitting circle to demonstrate an example of second-order least squares identification. It is known that the general formula of a circle is ( x ? a ) 2 + ( y ? b ) 2 […]
Tag: equation
Matlab calculates the solution of Ax=b, a ready-made tool for solving linear equations
1. Matlab solution Ax=b Only the simplest way is written, where b needs to be a column vector, and semicolons are used to separate elements; Ax = b where the matrix A(nxn) and the column vector b(n) are known; the solution of the system of equations is stored in x, written in matlab: > x=A\b […]
Score-based diffusion model code example for stochastic differential equations
Score-Based Generative Modeling through Stochastic Differential Equations The score-based diffusion model is a method for estimating the gradient of data distribution. It can generate images of the same high quality as GAN without the need for adversarial training. From the article: Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. […]
Advanced Python Algorithm: Construction of multi-stage decision-making problems and state transition equations
Advanced Python Algorithm: Construction of multi-stage decision-making problems and state transition equations Introduction 1. Introduction to multi-stage decision-making problems 2. Basics of dynamic programming 3. State transition equation 4. Case: Production planning problem 5. Python implementation 6. Summary Introduction Multi-stage decision-making problems are a type of problem that require a series of decisions to be […]
Root delimitation method for nonlinear equations (C++)
Article directory Graphical method General steps Implement code Case Analysis dichotomy General steps Implement code Case Analysis Trial position method Implement code Case Analysis Solving the roots of nonlinear equations is another very important problem in scientific research and engineering calculations. Whether it is solving differential equations in mathematical theory, optimization problems, numerical simulations, or […]
Calculation Methods: Initial Value Problems of Ordinary Differential Equations
This article refers to Professor Li Guicheng’s “Computational Methods” Derivation of Euler’s formula In ordinary differential initial value problems (1) Discretization method based on numerical differentiation If you change the DerivativeUse dot is approximately substituted, then we have . Where And because , it can be solved (2) Discretization method based on numerical integration Change […]
Forward difference format for parabolic equations
Article directory Preface 1. Introduction to the problem 2. Forward difference format 1. Meshing 2. Difference quotient instead of derivative 3. Truncation error and stability 3. Examples and MATLAB code implementation Due to my limited level, please criticize and correct any mistakes! You can also refer to my know-it-all blog link: [link](https://www.zhihu.com/people/xiao-jun-74-20) Foreword This article […]
Solving a system of linear equations in python implements the direct decomposition method (Doolittle, Kraut, chasing method)
1. Doolittle decomposition The Doolittle decomposition method is a method of decomposing a matrix into a lower triangular matrix L and an upper triangular matrix U. It is a special form of LU decomposition and is commonly used in calculations such as solving systems of linear equations and matrix inversion. The basic concepts of Doolittle […]
Solving a system of linear equations using Python to implement the elimination method (Gaussian elimination, column pivot, Gaussian Jordan)
1. Gaussian elimination method Gaussian elimination method is a basic method for solving linear equations. Its main idea is to convert the original coefficient matrix into an upper triangular matrix or lower triangular matrix through matrix transformation, and then solve the linear equations through back substitution and other methods. solution. Specifically, the Gaussian elimination method […]
Solve linear equations using Python to implement iterative methods (Jacobi iteration, Gauss-Seidel iteration, relaxation iteration)
1. Jacobi iteration The Jacobi iteration method is an iterative algorithm for solving systems of linear equations. It belongs to the direct iteration method among the iterative methods, and it approximates the solution of the linear equation system by continuously updating the solution vector iteratively. The basic concepts of Jacobi iteration method are as follows: […]