Self-learning Algorithm And Its Application

Self-learning algorithm that has the ability of the self-learning, and not only has a higher adapatability and accuracy, but also provides a number of difficult problems to solve new methods. In this dissertation, we carried out a further research about the solutions of the linear equations, numerical calculation and optimization of digital filter, which has a important significance on theory and practical application. The main works are as follows:(1)To study the researching of linear equations that is based on self-learning algorithm. It uses the three algorithms that respectively are gradient descent method, conjugate gradient method and the recursive least squares method to train the weight of neural network, and the weight vector is the needed solution of this linear equations.(2)To study the researching of numerical integration that is based on curve fitting. Similarly, It uses the polynomical curve fitting of three algorithms that respectively are gradient descent method, conjugate gradient method and the recursive least squares method to calculate the definite integration. It uses the three algorithms to replace the traditional algorithms to obtain the undetermined coefficient of the polynomial model. Finally, the famous formula, Newton-Leibniz formula, is used to obtain the original function, which is the polynomial as being function, so that achieveing the purpose of solving the numerical integration.(3)To study three optimized algorithms of FIR digital filter design. These three algorithms make the amplitude-frequency characteristics of designed FIR digital filter of linear phase as much as possible close to the amplitude-frequency characteristics of the ideal filter, and expresse magnitude function of the FIR digital filter with linear phase as a linear combination of the cosine basis functions. So the problem of filtering optimizations is transformed into optimizing the coefficient, then respectively using gradient descent method and the recursive least squares method train the coefficients of neural network of the cosine basis functions, and conjugate gradient method compute the weighting coefficients of the cosine basis functions, thus obtaining unit impulse of FIR filter.The simulation results show that the paper using the gradient descent method, conjugate gradient method and recursive least squares algorithm to solve the solutions of the linear equations, polynomial curve fitting and optimization of FIR digital filter designing, achieved good results. Particularly the using of recursive least squares algorithm solve the problem of Morbid equations, and the problem of noise filtering fitting. It has an important application in random noise filtering and morbid Equations fields.