简介:Inthispaperasimulatedannealing(SA)algorithmispresentedforthe0/1mul-tidimensionalknapsackproblem.Problem-specificknowledgeisincorporatedinthealgorithmdescriptionandevaluationofparametersinordertolookintotheperfor-manceoffinite-timeimplementationsofSA.ComputationalresultsshowthatSAper-formsmuchbetterthanageneticalgorithmintermsofsolutiontime,whilsthavingamodestlossofsolutionquality.
简介:Letf(x)∈C[-1,1],pn*(x)bethebestapproximationpolynomialofdegreentof(x).G.Iorentzconjecturedthatifforalln,p2n*(x)=p2n+1*(x),thenfiseven;andifp2n+1*(x)=p2n+2*(x),po*(z)=0,thenfisodd.Inthispaper,itisprovedthat,undertheL1-norm,theLorentzconjectureisvalidconditionally,i.e.if(i)(1-x2)f(x)canbeextendedtoanabsolutelyconvergentTehebyshevsories;(ii)foreveryn,f(x)-p2n+1*(x)hasexactly2n+2zeros(or,inthearcondsituation,f(x)-p2n+2*(x)hasexaetly2n+3zeros),thenLorentzconjectureisvalid.
简介:本文讨论矩阵方程ATX+xTA=C的一般解及其最佳逼近解的正交投影迭代解法.首先,利用矩阵的结构特点及相关性质,并借助矩阵空间的相关理论,给出求该矩阵方程一般解正交投影迭代算法;其次,根据奇异值分解、F-范数正交变换不变性证明算法的收敛性并推导出算法的收敛速率估计式,当方程相容时,该算法收敛于问题的极小范数解,且对该算法稍加修改,就可得到相应最佳逼近解;最后,用数值实例验证算法的有效性.
简介:本文证明第二种服务可选的M/M/1排队模型的主算子的点谱包含一个区间(-α,0),α〉0.此结果表明该主算子生成的C_0-半群不是紧算子,甚至不是最终紧算子.本文的结果与我们以前的结果合并后得到:(i)该C_0-半群的本质增长界为0.从而,该C_0-半群不是拟紧算子.(ii)该模型的时间依赖解不可能指数收敛于其稳态解.(iii)该C_0-半群的本质谱半径等于1.
简介:SupposethatwewanttoapproximatefC[0,1]bypolynomialsinPn,usingonlyitsvaluesonXn={i/n,0≤i≤n}.ThiscanbedonebytheLagrangeinterpolantLnfortheclassicalBernsteinpolynomialBnf.But,whenntendstoinfinity,LnfdoesnotconvergetofingeneralandtheconvergenceofBnftofisveryslow.WedefineafamilyofoperatorsBkn,n≥k,whichareintermediateonesbetweenB(0)n=B1n=BnandBnn=Ln,andwestudysomeoftheirproperties.Inparticular,weproveaVoronovskaja-typetheoremwhichassertsthatBknf-f=0(n-[(k+2)/2)forfsufficientlyregular.Moreover,B(k)nfusesonlyvaluesofBnfanditsderivatiesandcanbecomputedbyDeCasteljauorsubdivisionalgorithms.