linear adj. 1.線的,直線的。 2.長度的。 3.【數(shù)學】一次的,線性的。 4.【動、植】線狀的;細長的。 5.由線條組成的,以線條為主的,強調線條的。 linear amplification 直線放大。 a linear equation 一次方程式。 a linear leaf 線形葉。 linear arts 線條藝術。
A class of global convergent memory gradient methods and its linear convergence rate 一類全局收斂的記憶梯度法及其線性收斂性
The convergence of the refined non - interior continuation method for ncps is analyzed , the same global linear convergence as chen - xiu ' s is obtained 得到了與chen - xiu同樣的全局線性收斂,推廣了chen - xiu的局部超線性收斂到局部二次收斂。
Without the strict feasibility of the initial points and iteration points , the algorithm is shown to possess both polynomial - time complexity and q - linear convergence 該算法不要求初始點及迭代點的可行性且具有q -線性收斂速度和多項式時間復雜性。
Third , by means of smale , s point estimates theorem , the existence and the convergence theorem of broyden , s iteration is given , the method has less calculation and the speed of super linear convergence for solving the nonlinear equations with nondifferential terms under the point estimates or weak condition 第三,本文利用smale提出的點估計理論,給出了在點估計和弱條件下,用計算量小、具有超線性收斂速度的broyden方法來求解帶不可微項的非線性方程,給出了存在性收斂性定理及相應的證明。
Using the conic function model local approximation , w . cdavidon ( 1980 ) proposed a class of iterative algorithms with modified matrix combining function value , furthermore under the theory d . c . sorensen has used local quadratic approximation method , then applying collinear scaling idea improving on the above algorithm and generalizing it , getting a class of collinear scaling algorithm , unifying former quasi - newton . in the paper , using local quadratic approximation method , the first , constructing the new collinear scaling gene , getting a class of the new collinear scaling algorithm with briefness and numerical stability , . , we discusses some properties of the algorithm and its local linear convergence , q - superlinear convergence and the whole convergence ; secondly we have made numerical experimentation and numerical analysis ; the last , we have done much discussion for collinear scaling idea and given the several new collinear scaling algorithm 本文的工作就是基于局部二次逼近原理,首先通過構造新的共線調比因子,得到了一類新的更簡潔,數(shù)值穩(wěn)定性更好的共線調比算法,進而我們給出了本共線調比算法的局部收斂性,全局收斂性以及算法q -超線性速度的理論證明;其次,用經(jīng)典的無約束優(yōu)化五大考核函數(shù)就本共線調比算法進行了數(shù)值試驗和數(shù)值分析;最后,就局部二次逼近思想,進行共線調比算法思想進行更廣泛的討論,給出了幾個新共線調比算法。
2 . 4 linear convergence assumption ( h2 . 2 ) : let f ( x ) : rn - > r be twice continuously differ - entiable in some domain of x * which is the minimal point of f ( x ) , and exists e > 0 , m > m > 0 , if x - x * | | < holds , then the following inequality is satisfied , lemma 2 . 2 1若假設1成立,則算法或有限步終止于問題的穩(wěn)定點,或產生無窮點列沁k其任意極限點都是問題的穩(wěn)定點。 2 、 4線性收斂性假設2 2 :設八)在極小點”的領域內二次連續(xù)可微,且玉0 , m x 0 ,使得當iix ?工叫。