Newton. m
% Program 2.5 (Newton-Raphson iteration) function [P0, err, K, y] = Newton (F, DF, P0, Delta, Epsilon, max1) % input-F is the object function input as a string 'F' %-DF is the derivative of F input as a string 'df '%-P0 is the initial approximation to a zero of F %-delta is the tolerance for P0 %-Epsilon is the tolerance for the function values Y %
After learning the Newton iteration method, we compared it with MATLAB to verify the convergence rate.
First, the Newton Iteration Method
% Compare Newton Iteration Method,Function [x, I] = newtonmethod (x0, F, EP, Nmax) % x0-initial value, F-test function, EP-precision, Nmax-Maximum number of iterationsI = 1;X (1) = x0;While (I [G1, G2] = f (x (I ));If ABS (
Newton Iterative Method!/*============================================================Title: Newton Iterative method is used to solve the approximate solution of 3*x*x*x-2*x*x-16=0.============================================================*/#include #include #define E 1e-8Double HS (Double x){return (3*X*X*X-2*X*X-16);Original function}Double DHS (double x){return (9*X*X-4*X);Guide function}void Main (){D
1. Dichotomy method (first-order guide)Dichotomy is the method of using the first derivative of the objective function to compress the interval continuously, so in addition to asking F to be a single-peak function, f (x) is continuously differentiable.(1) Determine the midpoint of the initial interval x (0) = (a0+b0)/2. And then calculates the first derivative F ' (x (0)) at x (0) at f (x), if f ' (x (0)) >0, the minimum point is located on the left side of x (0), that is, the interval of the mi
Http://hi.baidu.com/aillieo/blog/item/0800e2a10ac9a59647106493.html
The known nonlinear equations are as follows:3 * x1-cos (X2 * X3)-1/2 = 0
X1 ^ 2-81*(X2 + 0.1) ^ 2 + sin (X3) + 1.06 = 0
Exp (-X1 * x2) + 20 * X3 + (10 * pi-3)/3 = 0
The accuracy of the solution must reach 0.00001.
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First, create the function fun
The storage equations program saves fun. m to the working path as follows:
Function f = fun (X );
% Defines the nonlinear equations as follows:
% Variab
2 weeksI am dead in these five physical engines.I can't say I understand it very well.A simple understanding
What I want to say most is that docization is really important ....Among the five, novodex is the best documented.Very detailed, including the idea of engine implementation. Every member of each class has a clear explanation of what it is.The other four are getting worse.The worst keys are tokamak and bullet.Where Tokamak is the differenceI can't even use official forums, and I still hav
You are welcome to reprint it. Please indicate the source, huichiro.Summary
This article will give a brief review of the origins of the quasi-Newton method L-BFGS, and then its implementation in Spark mllib for source code reading.Mathematical Principles of the quasi-Newton Method
Code Implementation
The regularization method used in the L-BFGS algorithm is squaredl2updater.
The breezelbfgs function
Evaluate the square root of N. Assume that x 0 = 1 is the predicted value. Then, calculate the X1 according to the following formula, then substitute X 1 into the right of the formula, and continue to obtain the X2... After an effective iteration, the square root of N can be obtained, XK + 1.Let's verify the accuracy of this clever method and calculate the square root of 2 (computed by mathomatic)1-> x_new = (x_old + Y/x_old)/2Y(X_old + -----)X_old#1: x_new = ---------------21-> calculate x_old
1. Newton Iteration Method:
The method for finding a solid root near x0 by using the Newton Iteration Method f (x) = 0 is(1) Select an approximate root X1 that is close to X;(2) Use X1 to obtain F (X1 ). In ry, x = X1 is used, and f (x) is used in F (X1 );(3) f (X1) is used as the tangent of f (x), and the X axis is X 2. You can use the formula to obtain X2. Therefore(4) use X2 to obtain F (X2 );(5) then f
Open Class at MIT [Introduction to Computer science and programming Using Python] 6.00.1x, Eric Grimson has mentioned that the idea of iterative algorithms is to move the current iteration point in the correct direction to a certain "step", and then verify whether the target value meets certain requirements. At the same time, "direction" and "step size" are the main concerns of different optimization algorithms two aspects. In addition, we also care about the convergence rate of the different op
Link to the question: Ultraviolet A 10428-the roots
Given a n-times polynomial, all solutions are obtained.
Solution: Newton Iteration Method. For any given X, the Newton iteration method can be used to obtain the nearest x solution x0. After finding a solution, use polynomial division to remove X? Continue to solve the problem after x0.
Newton Iteration Method
In this paper, we describe the method of Python to compute Newton iterative polynomial. Share to everyone for your reference. The implementation method is as follows:
"P = Evalpoly (a,xdata,x). Evaluates Newton ' s polynomial p at x. The coefficient vector ' a ' can is computed by the function ' coeffts '. A = Coeffts (xdata,ydata). Computes the coefficients of
Poj 3111 K best
The weight and value of N items are WI and VI. K items are selected to maximize the value per unit of weight.
Question:
1. Binary practice
2. Newton Iteration
Efficiency Comparison:
Binary practice:
Converting to judging whether a collection of K items exists meets the following conditions:
SIGMA (vi)/SIGMA (WI)> = X {vi, wi}
--> Simga (Vi-x * WI)> = 0
In this way, we sort YI = vi-x * WI {1
If sum (yi) {1
Then we can find K ite
Logistic Regression and Newton ' s MethodJob Link: http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=DeepLearningdoc=exercises/ex4/ Ex4.htmlThe data were 40 students admitted to the university and 40 children who did not enter the university in two test scores, and whether they passed the label.Based on the data, these two Tests were established with a two classification model of whether or not to enter the university.In the two cla
look at the defined cost function J (θ ):
We want to use the Newton's method to obtain the minimum value of Cost Function J (θ. Recall that the iteration rule of θ in Newton's method is:
In logistic regression, the gradient and Hessian methods are as follows:
Note that the preceding formula is written in Vector Form.
Where, the vector is n + 1*1, which is a matrix of N + 1 * n + 1.
And scalar.
Implementation
Follow the methods described in the Newton's method described
, and the other is that the number of iterations required cannot be determined. In the former case, a fixed number of loops can be constructed to control the iterative process, and in the latter case, further analysis is needed to conclude the conditions that can be used to end the iterative process.Next, I present a typical case of an iterative algorithm----Newton-Raphson (Kristinn) methodNewton-Raphson (Kristinn) method, also known as Newton's itera
Newton Iterative Method!/*============================================================Title: Newton Iterative method is used to solve the approximate solution of 3*x*x*x-2*x*x-16=0.============================================================*/#include #include #define E 1e-8Double HS (Double x){return (3*X*X*X-2*X*X-16);Original function}Double DHS (double x){return (9*X*X-4*X);Guide function}void Main (){D
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