Machine learning successive descent method (machine learning algorithm principle and practice) Zheng Jie

Definition of successive descent method:

1. For a given set of equations, use the formula:
   
   where k is the number of iterations (k=0,1,2,... ）
   The method of finding approximate solution by stepwise generation is called iterative method
2. If it exists (recorded as), it is said that this iterative method converges, obviously is the solution of the equations, otherwise called this iterative method divergence.
3. Study the convergence of {}. Introducing Error Vectors:
   
   Get:
   
   Recursion gets:
   
   To investigate the convergence of {}, we should study the conditions of B.

The following gives the Python implementation

#-*-Coding:utf-8-*-
Import NumPy as NP
From numpy Import *
From common_libs Import *
Import Matplotlib.pyplot as Plt

#消元发求解方程组的解
#求解元方程
Def method_nomal ():
A=mat ([[8,-3,2],
[4,11,-1],
[6,3,12]])
B=mat ([20,33,36])

Result=linalg.solve (A,B.T)
Print result

#迭代法进行计算
def interationmethod (n,b0,f):
Error = 1.0e-6 # iteration Threshold
steps = 100 # Number of iterations
Xk=zeros ((n,1))
Errorlist=[]
For I in range (steps):
Xk_1=xk
Xk=b0*xk+f
Errorlist.append (Linalg.norm (XK_1-XK))
If Errorlist[-1]<error:
Print i+1
Break
Print XK
Return i,errorlist

Method_nomal ()
B0=mat ([[0.0,3.0/8,-2.0/8],
[ -4.0/11,0.0,1.0/11],
[ -6.0/12,-3.0/12,0.0]])
Print (B0)
F=mat ([20.0/8,33.0/11,36.0/12])
[K,errorlist]=interationmethod (3,b0,f)

# Plot Scatter plots
matpts= Zeros ((2,k+1))
Matpts[0]=linspace (1,k+1,k+1)
Print Matpts[0]
Matpts[1]=array (errorlist)
Drawscatter (plt,matpts)
Plt.show ()

Machine learning successive descent method (machine learning algorithm principle and practice) Zheng Jie