本文選題：自學(xué)習(xí) + 線性方程組�。� 參考：《長沙理工大學(xué)》2015年碩士論文

【摘要】：自學(xué)習(xí)算法是一種具有自學(xué)習(xí)能力的算法,不僅具有更高的適應(yīng)性與精確性,而且還提供了解決一些疑難問題的新方法。該論文對實際應(yīng)用中所涉及的線性方程組的求解、數(shù)值積分的計算和濾波器的優(yōu)化設(shè)計等問題進行了深入的研究,具有較強的理論和實際意義。論文主要研究內(nèi)容如下:(1)對基于自學(xué)習(xí)算法的線性方程組求解進行研究。采用梯度下降法、共軛梯度法和遞推最小二乘法這三種算法分別對神經(jīng)網(wǎng)絡(luò)權(quán)值進行訓(xùn)練,得到的權(quán)值向量就是所求方程組的解。(2)對基于曲線擬合的數(shù)值積分進行研究。同樣,論文采用梯度下降法、共軛梯度法和遞推最小二乘法這三種多項式曲線擬合方法對定積分進行計算。用這三種算法取代傳統(tǒng)算法從而得到多項式模型的待定系數(shù)。最后采用著名的牛頓-萊布尼茲公式獲得以多項式為被積函數(shù)的原函數(shù),從而達到求解數(shù)值積分的目的。(3)研究了三種FIR線性相位數(shù)字濾波器的優(yōu)化設(shè)計算法。這三種算法都是使待設(shè)計的FIR線性相位數(shù)字濾波器的幅頻特性盡可能地逼近理想濾波器的幅頻特性,將幅度函數(shù)表示成余弦基函數(shù)的線性組合,因此,濾波優(yōu)化問題就轉(zhuǎn)化為求解余弦基函數(shù)的線性組合的系數(shù)問題,然后分別用梯度下降法和遞推最小二乘法訓(xùn)練余弦基函數(shù)的神經(jīng)網(wǎng)絡(luò)系數(shù),共軛梯度法計算余弦基函數(shù)的加權(quán)系數(shù),從而獲得FIR濾波器的單位脈沖響應(yīng)。仿真結(jié)果表明,論文利用梯度下降法、共軛梯度法和遞推最小二乘法等三種算法分別求解線性方程組、多項式曲線擬合以及FIR數(shù)字濾波器優(yōu)化設(shè)計,取得了良好結(jié)果。特別是使用遞推最小二乘法解決了病態(tài)方程組的難題,以及曲線擬合的噪聲濾波問題。在隨機噪聲濾波與病態(tài)方程組求解領(lǐng)域具有重要的應(yīng)用價值。
[Abstract]:Self-learning algorithm is an algorithm with self-learning ability, which not only has higher adaptability and accuracy, but also provides a new method to solve some difficult problems. In this paper, the solution of linear equations, the calculation of numerical integrals and the optimal design of filters are deeply studied, which is of great theoretical and practical significance. The main contents of this paper are as follows: (1) the solution of linear equations based on self-learning algorithm is studied. The weights of neural networks are trained by gradient descent method, conjugate gradient method and recursive least square method, respectively. The obtained weight vector is the solution of the equations. 2) the numerical integration based on curve fitting is studied. Similarly, three polynomial curve fitting methods, i.e. gradient descent method, conjugate gradient method and recursive least square method, are used to calculate the definite integral. The undetermined coefficients of the polynomial model are obtained by replacing the traditional algorithms with these three algorithms. Finally, by using the famous Newton-Leibniz formula, we obtain the original function with polynomial as the integral function, thus achieving the purpose of solving the numerical integral.) three optimal design algorithms for FIR linear phase digital filters are studied. These three algorithms make the amplitude-frequency characteristic of the FIR linear phase digital filter to be designed as close as possible to the ideal filter's amplitude-frequency characteristic. The amplitude function is expressed as a linear combination of the cosine basis function. The problem of filtering optimization is transformed into the problem of solving the linear combination coefficients of cosine basis functions, and then the neural network coefficients of cosine basis functions are trained by gradient descent method and recursive least square method, respectively. The conjugate gradient method is used to calculate the weighted coefficients of the cosine basis function, and the unit impulse response of the FIR filter is obtained. The simulation results show that three algorithms, I. e. Gradient descent method, conjugate gradient method and recursive least square method, are used to solve linear equations, polynomial curve fitting and FIR digital filter optimization, respectively, and good results are obtained. In particular, the recursive least square method is used to solve the problem of ill-conditioned equations and the noise filtering problem of curve fitting. It has important application value in the field of stochastic noise filtering and ill-conditioned equations.
【學(xué)位授予單位】：長沙理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TN713.7;TP183

【參考文獻】

相關(guān)期刊論文 前10條

1 雷旎;劉峰;曾U喺，

本文編號：1813050