The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理論成果主要包括：(1)對于對偶樹二進(jìn)制系數(shù)復(fù)數(shù)小波，利用Hilbert變換對性質(zhì)、完全重構(gòu)條件并結(jié)合新的提升格式構(gòu)造研究了含參系數(shù)多進(jìn)制小波構(gòu)造方法丁香婷五月，作為特例得到具有線性相位的對偶樹二進(jìn)制系數(shù)復(fù)數(shù)小波構(gòu)造方法亚洲愉拍一区二区精品；(2)對于廣義離散傅立葉變換與正弦變換對角化系統(tǒng)，提出了高效美女18网站、快速的多重網(wǎng)格算法，理論上證明了算法的收斂性欧美日本韩国A片三级片色哟哟；(3)研究了Toeplitz矩陣在多進(jìn)制小波變換下的代數(shù)結(jié)構(gòu)日韩高清美女自拍视频网站在线观看，驗(yàn)證了多項(xiàng)式生成函數(shù)構(gòu)成的Toeplitz系統(tǒng)在小波變換下的稀疏帶寬性質(zhì)，從而建立基于小波變換求解Toeplitz系統(tǒng)的快速求解方法黄色大片最新网址品尚网，運(yùn)算量級控制在O99玖玖国产精品视频，其中N為系統(tǒng)的階。

Thesolutions compose self-contained inner product space (weight function is constant 1),i.e., they are basic series of Hilbert space; hence any internal waves could beexpanded into generalized Fourier series. With difference method, Sturm-Liouvilleequation is transformed to matrix eigenvalue problem. Each eigenvalue is related to ahorizontal wave number, and relevant solution is a certain mode of internal wave.

其解系構(gòu)成完備的加權(quán)(權(quán)函數(shù)為1)內(nèi)積空間偷玩朋友的醉酒人妻中文字幕,，即Hilbert空間日韩一区二区精品，從而內(nèi)波現(xiàn)象可以展成該解系的廣義Fourier級數(shù)；采用差分方法性交毛片视频免费看，將 Sturm-Liouville 方程轉(zhuǎn)化為矩陣特征值問題欧洲精品乱码久久久久，每一個特征值對應(yīng)一個內(nèi)波波數(shù)，該特征值對應(yīng)的解則是內(nèi)波的某一模態(tài)福利视频一区二区三区。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先欧美另类在线观看，提出了含Hilbert核的第一類奇異積分方程的小波伽遼金(Wavelet-Galerkin)數(shù)值算法，該算法中利用了L~2([091在线人人艹，1])上的周期小波和Hilbert核的特點(diǎn)進(jìn)行處理一级A片国产孕妇，使得剛性矩陣維數(shù)降低并且通過閾值使得它更加稀疏，減少了計(jì)算量中文字幕观看；由于Hilbert核的奇異性欧美高潮抽搐免费A片大全，通過Tikhonov正則化方法求解所得到的剛性方程組，給出了收斂性和數(shù)值結(jié)果一a黄色视频；其次黄片视频兔费，對標(biāo)準(zhǔn)的一維逆熱傳導(dǎo)方程給出了一種基于Fourier正則化方法，給出了理論證明及其誤差估計(jì)国产清纯白嫩大学生正在播放，解決了文獻(xiàn)中算法與理論誤差估計(jì)的不相匹配的現(xiàn)象黄片免费直接看的色色小视频，該正則化方法不僅保留了測量數(shù)據(jù)的部分高頻成份，且與文獻(xiàn)中的算法具有同樣的計(jì)算量和誤差估計(jì)操操网。

hilbert matrix：希耳伯特矩陣

hilbert integral 希耳伯特積分 | hilbert matrix 希耳伯特矩陣 | hilbert modular form 希耳伯特模形式

hilbert matrix：希爾柏特矩陣

Hilbert basis 希爾柏特基底 | Hilbert matrix 希爾柏特矩陣 | Hilbert space 席柏特空問

Hilbert-Matrix Hilbert matrix：希耳伯特矩陣

Hilbert-Kurve Hilbert curve 希耳伯特曲線 | Hilbert-Matrix Hilbert matrix 希耳伯特矩陣 | Hilbert-Polynom Hilbert polynomial 希耳伯特多項(xiàng)式