convergence in norm 中文意思是什麼

convergence in norm 解釋
依范數收斂
  • convergence : n. 1. 聚合，會聚，輻輳，匯合。2. 集合點；【數、物】收斂；【生物學】趨同（現象）。
  • in : adv 1 朝里，向內，在內。 A coat with a furry side in有皮裡子的外衣。 Come in please 請進來。 The ...
  • norm : n. 1. 規范，模範；準則；（教育）標準。2. （勞動）定額；【數學】模方；范數。
  1. Chapter 2 of this paper, by using a new method of proof, we obtain the weak ergodic convergence theorem for general semigroups of asymptotically nonexpansive type semigroups in reflexive banach space. by theorem 2. 1 of chapter 1 we get the weak ergodic convergence theorem of almost orbit for general semigroups of asymptotically nonexpansive type semigroups in reflexive banach space. by this method of proof, we give the weak ergodic convergence theorems for right reversible semigroups. by theorem 2. 1 of chapter l, we generalize the result to almost orbit case. so we can remove a key supposition that almost orbit is almost asymptotically isometric. it includes all commutative semigroups cases. baillon [ 8 ], hirano and takahashi [ 9 ] gave nonlinear retraction theorems for nonexpansive semigroups. recently mizoguchi and takahashi [ 10 ] proved a nonlinear ergodic retraction theorem for lipschitzian semigroups. hirano and kido and takahashi [ 11 ], hirano [ 12 ] gave nonlinear retraction theorems for nonexpansive mappings in uniformly convex banach spaces with frechet differentiable norm. in 1997, li and ma [ 16 ] proved the ergodic retraction theorem for general semitopological semigroups in hilbert space without the conditions that the domain is closed and convex, which greatly extended the fields of applications of ergodic theory. chapter 2 of this paper, we obtain the ergodic retraction theorem for general semigroups and almost orbits of asymptotically nonexpansive type semigroups in reflexive banach spaces. and we give the ergodic retraction theorem for almost orbits of right reversible semitopological semigroups

    近年來， bruck [ 5 ] ， reich [ 6 ] ， oka [ 7 ]等在具frechet可微范數的一致凸banach空間中給出了非擴張及漸近非擴張映射及半群的遍歷收斂定理。 li和ma [ 13 ]在具frechet可微范數的自反banach空間中給出了一般交換漸近非擴張型拓撲半群的遍歷收斂定理，這是一個重大突破。本文第二章用一種新的證明方法在自反banach空間中，研究了揚州大學碩士學位論文2一般半群上的（ r ）類漸近非擴張型半群的弱遍歷收斂定理，即:定理3 . 1設x是具性質（ f ）的實自反banach空間， c是x的非空有界閉凸子集， g為含單位元的一般半群， s =仕工， 。
  2. These geometric nonlinear behaviors such as the sag of inclined cables caused by their own dead weight, the interaction of large bending moment and axial forces in girders and towers, and the large displacement effects are considered during calculation. newton - raphson method and the displacement convergence norm are used to approach the solution iteratively

    計算過程中計及了拉索的垂度效應，彎矩和軸力對主梁和主塔的組合效應以及結構的大變形效應等幾何非線性影響因素，採用newton - raphson方法和位移收斂準則進行迭代求解。
  3. By using bruck ' s lemma [ 10 ], passty [ 31 ] extended the results of [ 1, 16 ] to uniformly convex banach space with a frechet differentiable norm. however, there existed more or less limitations in their methods adopted. by using new techniques, chapter2 of this paper discussed the weak convergence theorem for right reversible semigroup of asymptotically nonexpansive type semigroup and the corresponding theorem for its almost - orbit in the reflexive banach space with a frechet differentiable norm or opial property

    Feattieranddotson 16 ]和bose [ l ]通過使用opial引理17 }在具弱連續對偶映照的一致凸b ~ h空間中證明了漸近非擴張映照的弱收斂定理， passty 31通過使用bruck引理10 ]把1 ， 16 ]的結果推廣到具freehet可微范數的一致凸banach空間，然而，他們的證明存在著種種局限性。
  4. Reich [ 2 ] proved the ergodic theorems to nonexpansive semigroups in hilbert spaces. takahashi and zhang [ 3 ], tan and xu [ 4 ] extended baillon ' s theorem to asymptotically nonexpansive and asymptotically nonexpansive type semigroups in hilbert spaces. recently, reich [ 6 ], bruck [ 5 ], oka [ 7 ] gave the ergodic convergence theorems for nonexpansive, asymptotically nonexpansive mappings and semigroups in uniformly convex banach spaces with frechet differentiable norm. li and ma [ 13 ] obtained the ergodic convergence theorems for general commutative asymptotically nonexpansive type topological semigroups in reflexive banach space, which is a great breakthrough

    Baillon [ 1 ]首先在hilbert空間的非空凸閉子集上給出了非擴張映照的弱遍歷收斂定理。 baillon的定理引起了很多數學家的興趣， reich [ 2 ]在hilbert空間中證明了非擴張半群的遍歷收斂定理。 takahashi和zhang [ 3 ] ， tan和xu [ 4 ]分別將baillon的定理推廣到漸近非擴張半群及漸近非擴張型半群。
  5. A parabolic regularity ( viscosity method ) and difference schemes in the rectangle mesh is constructed and convergence rata is obtained in the norm l1. his approximation method is lately called kuznetsov approximation t

    85 ]得到補償緊引理，並推得著名的div一curl引理，他給出了當一致l加估計序列的任意嫡消失測度在式
  6. On the other hand, with traditional iterations and the conjugate gradient ( cg ) as smoothers, we can show the optimal convergence rate of the cascadic method in energy norm for 1 - d and 2 - d cases. when the mesh level is arbitrary, we use a duality argument and obtain the quasi - optimality of the algorithm only for 2 - d problems

    另一方面，採用傳統迭代子和共軛梯度法作為光滑子，我們證明了瀑布型多重網格法對一、二維非線性橢圓邊值問題，在能量范數下，均可獲得最優收斂階。
  7. In case of high input dimension system model, taking norm of input vector as the input of wavelet network instead of using tensor product method to construct wavelet network, which could solve the problems of high computation and curse of dimensionality. in the selecting of specific wavelet basis, this thesis first gets initial wavelet basis collection according to spectrum analysis, then gives the least squares regression algorithm to optimize wavelet basis collection based on the least estimation error criteria, which could also initialize the model parameters and increase the speed of convergence

    對于具體的模型小波基函數選擇，本文首先對樣本數據進行時頻域分析，根據小波基函數時頻空間覆蓋樣本時頻空間的原則，在小波框架中選擇建模所用的函數集，然後根據估計誤差最小準則，給出最小二乘回歸優選演算法以進一步優化小波基函數集。
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