[數] 最速下降法；[數] 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，推導出了相應的自適應算法。
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.
由于它采用非線性規劃中的最速下降法，因而存在極易陷入局部極小的缺陷。
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.
病态線性方程組的計算題，涉及Gauss消元法、雅可比疊代法、高斯-賽德爾疊代法、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優點是不需要存儲矩陣，而且收斂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.
文中的算例結果表明，混合算法與單純的共轭梯度法或最速下降法相比，具有收斂速度快、收斂範圍大、適應面寬等特點。
The learning method of hidden output layer weights is the steepest descent method and the one of input hidden layer weights is genetic algorithm.
隱層輸出層的權值用最速下降法學習，輸入層隱層的權值用遺傳算法進行學習。
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.
将最速下降法與共轭梯度法有機結合起來，構造出一種混合優化算法，并證明其全局收斂性。
The one-dimension projection algorithm, which is the steepest descent method, based on residual space for solving linear equations is analyzed in this paper.
分析了基于殘差空間求解線性方程組的一維投影算法、最速下降法和最小剩餘法。
The maximum likelihood estimation of such model is discussed, and an approximate solution is obtained with the steepest descent method.
文中讨論了這類模型參數的極大似然估計，并采用最陡下降法來求其近似解，模拟試驗證實此算法是有效。
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.
對于可以用延時二階模型來拟合的過程，使用一種智能采樣技術，結合階躍下降法，實現了對實時過程的線上模拟。
This algorithm splits the difference between the Newton method and the steepest descent method, which is suitable for neural network training.
該算法的本質是提供牛頓法的速度和保證收斂的最速下降法之間的一個折中，適合于性能指标是平方誤差的神經網絡訓練。
The algorithm which utilizes the Steepest Descent Method can give the estimation of displacement between two frames of image directly.
它對一定時間間隔内兩次采樣得到的圖象進行運算，用最陡梯度下降法直接疊代出圖象位移的估計值。
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) .
網絡隱層-輸出層的權值采取最速下降法學習，輸入層-隱層的權值采用遺傳算法進行學習；
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.
它的學習規則是使用最速下降法，通過反向傳播來不斷調整網絡的權值和阈值，使網絡的誤差平方和最小。
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 .
然後提出了一種新的LMS算法——改進的最陡下降法，該算法正是求最佳權矢量的一個簡單而有效的算法。
Three unconstrained optimization methods'steepest descent method, DFP variable metric algorithm and BFGS variable metric algorithm, are compared with each other.
文中比較了最速下降法、DFP變尺度法和BFGS變尺度法這三種無約束最優化算法；
By the steepest descent method, some meaningful results have been obtained in the calculation of the MFPT for a system with nonlinear drift.
利用最陡下降法簡化所得結果，處理了具有非線性漂移的隨機系統的MFPT問題。
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.
在浮點編碼遺傳算法中加入最速下降法，構成適于函數全局優化的混合遺傳算法。
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.
導出一種既有最速下降法的穩定性又有牛頓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.
在用傳統聚類方法得到初步的RBF隱節點參數之後，提出再用最陡下降法進行誤差反傳學習，進一步校正隱節點參數。
By steepest descent rule, a new method of selecting cutting plane equation has been given.
用最速下降規則，給出了選擇割平面的一個新方法。
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.
然後系統闡述了基本維納濾波原理和自適應濾波器的基本結構模型，接着在此基礎上結合最陡下降法引出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.
通過最速下降法求LOO上界的極小點來确定核參數是一種新的核參數選擇方法。
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該問題，通過計算機仿真，可以看到該方法與原來采用方法具有相似的結果，為工程應用提供了一種簡單、實用的方法。
最速下降法（steepest descent method）是一種用于無約束優化問題的疊代算法，其核心思想是通過沿目标函數在當前點的負梯度方向進行搜索，以最快速度逼近局部極小值點。該方法適用于連續可微且具有明确梯度表達式的函數優化場景。
最速下降法的數學基礎是梯度向量性質：函數在某點的梯度方向$ abla f(mathbf{x})$代表該點處函數值增長最快的方向，而負梯度方向$- abla f(mathbf{x})$則是函數值下降最快的方向。疊代公式為： $$ mathbf{x}_{k+1} = mathbf{x}_k - alpha_k abla f(mathbf{x}_k) $$ 其中步長$alpha_k$通過精确線搜索或回溯線搜索确定，以确保每次疊代後函數值嚴格減小（來源：Springer《最優化算法》）。
該算法在電氣工程中用于電力系統狀态估計（來源：IEEE Transactions on Power Systems），在機器學習中應用于邏輯回歸參數優化（來源：MIT《數值分析》課程講義），同時是共轭梯度法等高級優化算法的基礎框架。
對于強凸函數，最速下降法具有線性收斂速率，但其收斂速度受Hessian矩陣條件數影響顯著。當目标函數的等高線呈狹窄山谷狀時，算法可能産生鋸齒形收斂路徑（來源：Boyd《凸優化》）。
最速下降法（Steepest Descent Method）是一種用于無約束優化問題的疊代算法，主要用于尋找多元函數的局部最小值。其核心思想是在每一步疊代中，沿着當前點的負梯度方向（即函數下降最快的方向）進行搜索，通過調整步長逐步逼近極小值點。以下是詳細解釋：
以二次函數 $f(x) = frac{1}{2}x^T Q x - b^T x$ 為例（$Q$ 對稱正定）：
最速下降法通過沿負梯度方向疊代逼近極小值點，雖然簡單但受限于收斂速度。在實際應用中，常與其他方法（如共轭梯度法或拟牛頓法）結合以提升效率。
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