Backward error analysis of a class of the periodic symplectic matrices for eigenproblem 一類(lèi)周期辛矩陣對(duì)特征值問(wèn)題的向后誤差分析
They have a number of desirable properties not possessed by wavelets of daubechies type , namely : they have symmetry property ; the scaling function and physical space representation are identical ; expansion coefficients are easily computed ; in certain respects they are more accurate ; the functions ( but not their derivatives ) can be computed without solving an eigenproblem . the price to be paid for these advantages is the loss of orthogonality , interpolating wavelets are only biorthogonal 本文主要的研究成果是把一維的某些結(jié)論推廣到高維,分為以下四個(gè)方面: ( 1 )使用二元拉格朗日插值法構(gòu)造二元尺度函數(shù)和小波函數(shù),使其具有緊支性、對(duì)稱性以及函數(shù)展開(kāi)式的系數(shù)易于計(jì)算等優(yōu)點(diǎn)。唯一的缺陷是缺乏正交性。
Based on the properties of bisymmetric matrices , a class of constrained inverse eigenproblem and associated approximation problem for bisymmetric matrices were essentially decomposed into the same kind of subproblems for real symmetric matrices with smaller dimensions , and the solutions of the two problems were obtained by applying the conclusions of real symmetric matrices 摘要根據(jù)雙對(duì)稱矩陣的性質(zhì),將雙對(duì)稱矩陣的一類(lèi)約束逆特征值問(wèn)題及其逼近問(wèn)題分解成具有較小階數(shù)的實(shí)對(duì)稱矩陣的同類(lèi)子問(wèn)題,然后利用實(shí)對(duì)稱矩陣的結(jié)果導(dǎo)出雙對(duì)稱矩陣的這兩個(gè)問(wèn)題的解。