[数] 最速下降法；[数] 最陡下降法
The corresponding adaptive algorithm was derived based on the steepest descent method.
基于最陡下降方法，推导出了相应的自适应算法。
Since it adopt the steepest descent method in nonlinear programming, it has the drawback that easy converge to a local minimum point of the error function.
由于它采用非线性规划中的最速下降法，因而存在极易陷入局部极小的缺陷。
Morbid Linear Equations calculation problems involving Gauss elimination method, Jacobi' s iterative method, Gauss- Seidel iterative method, steepest descent method and conjugate gra***nt method.
病态线性方程组的计算题，涉及Gauss消元法、雅可比迭代法、高斯-赛德尔迭代法、最速下降法和共轭梯度法。
The key features of the conjugate gra***nt algorithms are that they require no matrix storage and they are faster than the steepest descent method.
共轭梯度算法最大的优点是不需要存储矩阵，而且收敛速度比最速下降法要快。
Compared with the conjugate method or the steepest descent method, the method has features with quick convergence rate, large convergence range and wide accommodation.
文中的算例结果表明，混合算法与单纯的共轭梯度法或最速下降法相比，具有收敛速度快、收敛范围大、适应面宽等特点。
The learning method of hidden output layer weights is the steepest descent method and the one of input hidden layer weights is genetic algorithm.
隐层输出层的权值用最速下降法学习，输入层隐层的权值用遗传算法进行学习。
Based on the steepest descent method and the conjugate gra***nt method, a hybrid algorithm is proposed in this paper, and its global convergence is proved.
将最速下降法与共轭梯度法有机结合起来，构造出一种混合优化算法，并证明其全局收敛性。
The one-dimension projection algorithm, which is the steepest descent method, based on residual space for solving linear equations is analyzed in this paper.
分析了基于残差空间求解线性方程组的一维投影算法、最速下降法和最小剩余法。
The maximum likelihood estimation of such model is discussed, and an approximate solution is obtained with the steepest descent method.
文中讨论了这类模型参数的极大似然估计，并采用最陡下降法来求其近似解，模拟试验证实此算法是有效。
An intelligent sampling technique coupled with the steepest descent method is implemented for on-line estimation of the process, which can be approximated by a second-order model with time delay.
对于可以用延时二阶模型来拟合的过程，使用一种智能采样技术，结合阶跃下降法，实现了对实时过程的在线模拟。
This algorithm splits the difference between the Newton method and the steepest descent method, which is suitable for neural network training.
该算法的本质是提供牛顿法的速度和保证收敛的最速下降法之间的一个折中，适合于性能指标是平方误差的神经网络训练。
The algorithm which utilizes the Steepest Descent Method can give the estimation of displacement between two frames of image directly.
它对一定时间间隔内两次采样得到的图象进行运算，用最陡梯度下降法直接迭代出图象位移的估计值。
The learning method of hidden-output layer weights is the steepest descent method and the one of input-hidden layer weights is genetic algorithm(GA) .
网络隐层-输出层的权值采取最速下降法学习，输入层-隐层的权值采用遗传算法进行学习；
Its learning rule is to use the steepest descent method, by back-propagation network to continuously adjust the weights and thresholds, so the network and the minimum sum of squared errors.
它的学习规则是使用最速下降法，通过反向传播来不断调整网络的权值和阈值，使网络的误差平方和最小。
Then modified steepest descent method which is a new LMS algorithm of adaptive filters is presented , This method is a ****** and effective algorithm to solve optimum coefficient .
然后提出了一种新的LMS算法——改进的最陡下降法，该算法正是求最佳权矢量的一个简单而有效的算法。
Three unconstrained optimization methods'steepest descent method, DFP variable metric algorithm and BFGS variable metric algorithm, are compared with each other.
文中比较了最速下降法、DFP变尺度法和BFGS变尺度法这三种无约束最优化算法；
By the steepest descent method, some meaningful results have been obtained in the calculation of the MFPT for a system with nonlinear drift.
利用最陡下降法简化所得结果，处理了具有非线性漂移的随机系统的MFPT问题。
A hybrid computational intellective algorithm for locating the global optima of function put forward by setting the steepest descent method in real-code genetic algorithm.
在浮点编码遗传算法中加入最速下降法，构成适于函数全局优化的混合遗传算法。
A improved BP neural network algorithm with the stability of the steepest descent method and the speed performance of the Newton approach method is educed.
导出一种既有最速下降法的稳定性又有牛顿法的快速性的新算法；
At first, the hidden node parameters of RBF are obtained by the classical clustering method; then those parameters are stu***d again by the method of steepest descent.
在用传统聚类方法得到初步的RBF隐节点参数之后，提出再用最陡下降法进行误差反传学习，进一步校正隐节点参数。
By steepest descent rule, a new method of selecting cutting plane equation has been given.
用最速下降规则，给出了选择割平面的一个新方法。
Then we explain basic theory of wiener filter and basic structure model of adaptive filter, and combine the method of steepest descent to deduce the LMS.
然后系统阐述了基本维纳滤波原理和自适应滤波器的基本结构模型，接着在此基础上结合最陡下降法引出LMS算法。
Minimizing the LOO upper bound is one of efficient method to select kernel-parameter. Usually, the steepest descent algorithm is used to find the minimum of LOO upper-bound.
通过最速下降法求LOO上界的极小点来确定核参数是一种新的核参数选择方法。
In this paper, the steepest descent arithmetic is used. The computer simulations results show that it is approximate to the common ones. The new method is a viable way in engineering applications.
文中采用最陡下降算法求解该问题，通过计算机仿真，可以看到该方法与原来采用方法具有相似的结果，为工程应用提供了一种简单、实用的方法。
最速下降法（steepest descent method）是一种用于无约束优化问题的迭代算法，其核心思想是通过沿目标函数在当前点的负梯度方向进行搜索，以最快速度逼近局部极小值点。该方法适用于连续可微且具有明确梯度表达式的函数优化场景。
最速下降法的数学基础是梯度向量性质：函数在某点的梯度方向$ abla f(mathbf{x})$代表该点处函数值增长最快的方向，而负梯度方向$- abla f(mathbf{x})$则是函数值下降最快的方向。迭代公式为： $$ mathbf{x}_{k+1} = mathbf{x}_k - alpha_k abla f(mathbf{x}_k) $$ 其中步长$alpha_k$通过精确线搜索或回溯线搜索确定，以确保每次迭代后函数值严格减小（来源：Springer《最优化算法》）。
该算法在电气工程中用于电力系统状态估计（来源：IEEE Transactions on Power Systems），在机器学习中应用于逻辑回归参数优化（来源：MIT《数值分析》课程讲义），同时是共轭梯度法等高级优化算法的基础框架。
对于强凸函数，最速下降法具有线性收敛速率，但其收敛速度受Hessian矩阵条件数影响显著。当目标函数的等高线呈狭窄山谷状时，算法可能产生锯齿形收敛路径（来源：Boyd《凸优化》）。
最速下降法（Steepest Descent Method）是一种用于无约束优化问题的迭代算法，主要用于寻找多元函数的局部最小值。其核心思想是在每一步迭代中，沿着当前点的负梯度方向（即函数下降最快的方向）进行搜索，通过调整步长逐步逼近极小值点。以下是详细解释：
以二次函数 $f(x) = frac{1}{2}x^T Q x - b^T x$ 为例（$Q$ 对称正定）：
最速下降法通过沿负梯度方向迭代逼近极小值点，虽然简单但受限于收敛速度。在实际应用中，常与其他方法（如共轭梯度法或拟牛顿法）结合以提升效率。
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