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1.
§ 1.Introduction Sincesecondorderellipticboundaryvalueproblemshavewideapplicationsinphysics ,thestudyofpositiveradialsolutionsforthesemilinearproblem (P) Δu(X) +g( |X|)f(u(X) ) =0 , R1<|X|<R2 ,u(X) =0 , |X|=R1or |X|=R2(whereR1>0 ,X∈Rn,n≥ 2 )hasbeenmadeforrecent 2 0years ;see [1— 5]forr… 相似文献
2.
Liu Zhongyun 《高等学校计算数学学报(英文版)》2000,9(1):61-70
1 IntroductionLetAbeann×nsymmetricpositivedefinitematrix .WeconsidertheiterativesolutionofalargelinearsystemofequationsAx=bbytheparallelmultisplittingmethod .ThemultisplittingmethodwasintroducedbyO’LearyandWhite[9] andfurtherstudiedbymanyotherauthors .Butt… 相似文献
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§ 1.Introduction WearegivenkindependentWishartdensitiesofthe (p +q)× (p +q)randomsymmetricpositivedefinitematricesG1,… ,Gktobeg(Gi) =Kexp -12 trR- 1i Gi Gi12 (ni- q-p- 1) ,(1 )wherei=1 ,… ,k,andRidenotesthepopulationcorrelationmatrixofthei thpopulationandKasagenericletterdenote… 相似文献
4.
§ 1 IntroductionConsiderthefollowingnonlinearoptimizationproblem :minimizef(x)subjecttoC(x) =0 , a≤x≤b ,( 1 .1 )wheref(x) :Rn→R ,C(x) =(c1(x) ,c2 (x) ,...,cm(x) ) T:Rn→Rm aretwicecontinuouslydifferentiable,m≤n ,a ,b∈Rn.Trustregionalgorithmsareveryeffectiveforsolvingnonlinearoptimi… 相似文献
5.
Additive Adjugate Preservers on the Matrices over Fields 总被引:3,自引:0,他引:3
§1.IntroductionSupposethatFisafieldandF*itsmultiplicativegroup.LetMn(F)andSn(F)bethespaceofaln×nmatricesandaln×nsymmetricmatr... 相似文献
6.
Wulan Hasi 《东北数学》1995,(3)
Hardy-LittlewoodTheoremsinMixedNormSpacesonBoundedSymmetricDomainofC~n¥(乌兰哈斯)WulanHasi(DepartmentofMathematics,InnerMongoliaN?.. 相似文献
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LetB ={0 ,1 }betheusualbinaryBooleanalgebra .ThematricesoverBarecalledBooleanmatrices.Ann×nBooleanmatrixAiscalledaprimitivematrixifthereexistsapositiveintegerksuchthatAk=J (whereJistheuniversalmatrix) .TheleastsuchkiscalledtheexponentofA ,denotedbyγ(A) . In proj… 相似文献
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本文讨论了积流形的P-形式上Laplace算子谱的唯一性问题,在紧Kachler流形乘积和紧Sasaki流形乘积的两类积流形中,CPn×CPn和S2n+1(1)×S2n+1(1)是P-形式上Laplacce算子谱特征。 相似文献
9.
Lagrange Interpolation on a Sphere 总被引:1,自引:0,他引:1
§ 1.Introduction LetnbeanonnegativeintegerandS ={(x ,y ,z)∈R3 |x2 + y2 +z2 =1 }betheunitsphereinR3 .P( 2 )n andP( 3 )n denotethespaceofallbivariatepolynomialsoftotaldegree≤nandthespaceofalltrivariatepolynomialsoftotaldegree≤nrespectively ,i.e .P( 2 )n =∑0≤i+j≤naijxiyj|aij ∈R ,P( 3 … 相似文献
10.
§ 1.Introduction Letabeameasurablefunction ,bea φ∈S(R)nonnegativefunction ,and 0 <r <∞ .Definecommutatorsasfollows :Cra( f) (x) =supx∈Q1|Q|∫Q|a(x) -a( y) |r|f( y) |dy ,( 1 .1 )andΦra( f) (x) =supε>0∫Rn|a(x) -a( y) |rφε( |x- y|)|f( y) |dy ,( 1 .2 )whereQdenotesacubeandφε(t) =1εnφ tε .Thesetwooperat… 相似文献
11.
In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation X + A*X?αA = Q with α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rates of convergence of the considered methods are obtained. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
12.
In this paper,Hermitian positive definite solutions of the nonlinear matrix equation X + A*X-qA = Q (q ≥ 1) are studied.Some new necessary and sufficient conditions for the existence of solutions are obtained.Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions,and the convergence analysis is also given.The theoretical results are illustrated by numerical examples. 相似文献
13.
In this paper, Hermitian positive definite solutions of the nonlinear matrix equation X + A^*X^-qA = Q (q≥1) are studied. Some new necessary and sufficient conditions for the existence of solutions are obtained. Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions, and the convergence analysis is also given. The theoretical results are illustrated by numerical examples. 相似文献
14.
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^*X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples. 相似文献
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16.
矩阵方程aX2+bX+cE=O的正定解和实对称解 总被引:3,自引:1,他引:2
给出了矩阵方程aX2+bX+cE=O,a,b,c∈R,a≠0有正定解,实对称解的充分必要条件及解的一般形式. 相似文献
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18.
We study the symmetric positive semidefinite solution of the matrix equation AX
1
A
T
+ BX
2
B
T
= C, where A is a given real m×n matrix, B is a given real m×p matrix, and C is a given real m×m matric, with m, n, p positive integers; and the bisymmetric positive semidefinite solution of the matrix equation D
T
XD = C, where D is a given real n×m matrix, C is a given real m×m matrix, with m, n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and
present necessary and sufficient conditions for guaranteeing the existence of these solutions.
Received December 17, 1999, Revised January 10, 2001, Accepted March 5, 2001 相似文献
19.
杨凯凡 《数学的实践与认识》2013,43(3)
研究了算子方程X(-1)+A(-1)+A+X+XtA=Q,的正算子解问题,给出了此类非线性算子方程正算子解的范围以及正算子解存在的一些充分必要条件,并用迭代的方法得到了方程的正算子解. 相似文献
20.
本文推广了文[1]的主要定理,给出了用低阶矩阵判定高阶矩阵正定的判定定理,同时给出了矩阵方程AX=B的反问题在正定矩阵类中解存在的充要条件及解的一般形式. 相似文献