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
Compared with the gradient descent method, Newton method has a faster convergence rate and second-order convergence in search space, that is to approximate the optimal solution with elliptical surface, and Newton method can be regarded as gradient descent method under two-times surface. Newton method for convex two times optimal problem, iterative one can get the
#include #include #include typedef struct DATA{float x;Float y;Structure of}data;//variable x and function value yData d[20];//up to 20 setsfloat f (int s,int t)//Newton interpolation to return to the plug-in{if (t==s+1)Return (D[T].Y-D[S].Y)/(d[t].x-d[s].x);ElseReturn (f (s+1,t)-F (s,t-1))/(d[t].x-d[s].x);}Float Newton (float x,int count){int n;while (1){coutcin>>n;if (nBreakElseSystem ("CLS");}Initialize
Ng's Courseware 1 also speaks of Newton's law, and its corresponding update rule is??????????H corresponds to Hessian matrixHttp://en.wikipedia.org/wiki/Hessian_matrix??http://aria42.com/blog/2014/12/understanding-lbfgs/Gives a more detailed explanation of Newton's Law:??Do the function Taylor expand http://en.wikipedia.org/wiki/Taylor_seriesCompare a single-variable function Taylor expansion formula:????Consider that we need to find a position where the first derivative is 0.??Consistent with t
Newton's iterative method, starting with a value, obtains the result in the way of infinite approximation.#include #include intMain () {DoubleADoubleX scanf"%LF", a);//Seek square root and cubic root of ax =2;/// square root //// while(Fabs (x*x-a) > (1e-6) {x = (x+a/x)/2; } printf ("%lf\n", x);/ //// cubic root/////////////x=1;//Starting from 1, of course, can also start from other numbers while(Fabs (x*x*x-a) > (1e-6)) {x = (2*x +a/(x*x))/3; } printf ("%lf\n", x);return 0;} Copyright
, english = 90, student = new Student {Name = "Newton" }}; TeacherChinese teacherChinese = new TeacherChinese (); // Chinese teacher Tea CherEnglish teacherEnglish = new TeacherEnglish (); // english teacher TeacherMathematics teacherMathematics = new TeacherMathematics (); // mathematics teacher TeacherTeacherHead teacherTeacherHead = new teacher (); // The class teacher // Newton's transcript is displayed. The teacher wants to know the result. Score
Iterative method/*==================================================================Title: Newton Iterative method to find the square root of a! Iterative formula: xn+1= (XN+A/XN)/2.==================================================================*/#include #include Main (){float a,x0,x1;int flag=1;while (flag){printf ("a=");scanf ("%f", a);if (a>=0)flag=0;Elseprintf ("You cannot enter the number of square root, please try again!") \n________________
1#include 2#include 3#include 4#include float.h>5#include 6 7 #definePi 3.14159265358979323846/* pi */8 #defineΕ1.0e-129 intMain ()Ten { One Doublex0 = PI;//the initial value taken A DoubleX1 =0.0;//with x0 calculated x1, the initial value is given 0 first . - DoubleFX =0.0;//f (x) - DoubleFXP =0.0;//derivative of f (x) the DoubleFaix =0.0;//computed results, Newton iteration format Faix =x-(FX/FXP) - inti =0;//number of iterat
also meets the initial maximum likelihood estimation requirements.Hessian MatrixDescribes the local curvature of a multivariate function.
The iterative form is as follows (solving the equation)
At the beginning, we will select a vertex as the iteration start point. Sometimes the selection of this vertex is critical because the Newton iteration method obtains the local optimal solution, as shown in figure
If the function only has one zero point, th
formula) to get the maximum value of f (x).There must be an F (x) 0 point for the three intervals consisting of the maximum points, and the 0 points can be obtained by Newton iterative method.Newton's iterative method is the constant use of a point tangent to fit the curve, the derivative of that point is the tangent slopeAnd so on, we can get an iterative method to find 0 points of the higher order function:To find the n-th function 0 points, need t
Newton's method is an iterative algorithm, the principle can be summed up in a sentence: if a * b = n, then the square root of n must be between A and BIn other words (A + B)/2, must be more accurate than aPackage puzzles.sqrt/** * Created by Bo on 2015/1/1. */import Scala.math.absobject Newton extends app{def sqrt (num:double): double = {def iter (guess:double): double = if (guess)) Guess else ITER (better (guess)) def ok (guess:double) = ABS (guess
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