由非顺序主子阵和缺损广义特征对构造对称三对角矩阵

本文讨论形如A_nX=λC_nX的方程,其中A_n是一个对称三对角矩阵,C_n是一个对角矩阵.对矩阵A_n进行3×3分块,给定A_n的一个非顺序主子阵A_(r+1,r+s),给定C_n和四个向量X_1=(x_1,…,x_r)',X_3=(x_(r+s+1),…,x_n)',Y_1=(y_1,…,y_r)',Y_3=(y_(r+s+1),…,y_n)'和两个不同实数λ,μ,构造一个对称三对角矩阵A_n和两个向量X_2=(x_(r+1),…,x_(r+s))',Y_2=(y_(r+1),…,y_(r+s))',满足A_nX=λC_nX和A_nY=μC_nY,其中X=(X_1',X_2',X_3')',Y=(Y_1',Y_2',Y_3')'.本文给出问题有解的条件,解的表达式和相应算法,并给出数值算例验证算法的有效性.     

ON INTERPOLATION OF A CERTAIN CLASS OF FUNCTIONS

I.StatementofResultsForarealaleta~ma-c(1,Ial).Lets21.WeuseG.todenotethes-dimensionalunitcube,and(:,')todenotethescalarproductofvectors:and,inH.Form(ml,',m.)EZsand^~(Al,',A.)EHwedenotel'II^=mtl...m:a.Inparticular,ifA=(A,',A),thenwewritellmJI'=IImll^.Fulthermore,forf=(TI,'.)r.)EH,letiff=lrlI ... Ir.].Letf~(n,',r.)ERswithfi20(i~1,',s),andletf(:)beasingle--valuedfunctionsuchthatf(xl,'sxit',x.)~f(xl,')xi 1,',x.),i~1,')s.Writefi=pi fi(i~1,',s),wherepi~fi~0iffi=0an…     

VARIATIONS ON A THEME BY EULER

1.IntroductionAHallliltolliansystemofdifferentialequationsonRZnisgivedbyP~~H,(P,q),q=HP(P,q),(1)wherep=(pl,'.,P.),q=(ql,',q.)eR"arethegeneralizedcoordinatesandmolllentarespectivelyandH(P,q)istheellergyofthesystem.Thesystem(1)canberewrittenasthecompactf…     

Optimal Interior and Local Error Estimates of a Recovered Gradient of Linear Elements on Nonuniform Triangulations

1.IntroductionConsideramodelellipticboundaryvalueproblemwhereflCRd,d=1,2,3,isaboundedpolyhedraldomainwithaLip8chitzboundaryfEL'(fl),aijareLipschitz-continuousfunctionsandthematrixA=(aij)issymmetricanduniformlypositivedefinitewithrespecttoxEn.Itisknownthatthefiniteelementmethodappliedto(1.1)mayproducesomesuperconvergencephenomenaeveniftheusedmeshesarenonuniform[5'8'9'1o'121.InarecentpaPer[61,aninteriorerrorestimatefortherecoveredgradientofGalerkinpiecewiselinearaPproximationshasbeenproposed…     

A TOBIN-TYPE ESTIMATE OF CENSORED LINEAR MODELS

1IntroductionConsiderthelinearregressioumodelcensoredfromtheleft:K=m{K,0}=rnax{Z:W ei,0},1Si5n,(1.1)whereZi=(1,X:),,15i5n,7o=(ac,P6)'(1'2)ThedimensionalityofXiisd21.WeobBerve(Xi,K)',1SiSn.Basedontheseobservations,wetrytogivesomeestimationofac,ortesthypothesisonit.Themodelwasfirstconsideredbycabin[llundertheassumptionthatelfe2,''arelid.withacommonnormaldistributionN(0,rs:).HedefinedtheMLEof7o,whichnowisusuallyknownastheTobinestimator.TheconsistencyOfthisestimatorwasestablishedbyAmend…     

GLOBAL EXISTENCE OF SOLUTIONS FOR A STRONGLY COUPLED REACTION-DIFFUSION SYSTEM

1IntroductionInthispaper,weinvestigatetheglobalexistencealldtllliqllellessofthesmoothsolutiolltotilefollowingIBVPHerefiCR'1isaboulldeddomainwithsllloothboundaryoff,alldal,uZarcunkllowllfullctiolls,QT=(0,T)xfi,ST=(0,T)xoff,Tisanarbitrarypositiveconstallt,R=(--co, co).BI.'Itk=orb(f,x:)% aam(t,x)'(Lk,kistheoutwardnormalderivative,AistheLaplacianoperator,7t(k=(%,....%)(k=1,2)arethegradients.nisanarbitrarypositiveinteger.IBVP(1.1)coillesfi.ommanymathematicalalldphysicalproblelll.Ill11],fo…     

BOUNDARY VALUE PROBLEMS TO A CLASS OF SINGULARLY PERTURBED NONLINEAR SYSTEM WITH TURNING POINTS

ConsidertheboundaryvalueproblemtothesingularlyperturbednonlinearsystemintheformofwhereEisasmallpositiveparameter,y=(yi,'..)y.),f=(fi,...)fn),A=(Al,'',A.)andB=(BI,sn).MohasdiscussedtheseDroblemsundervarioussituationsusingthemethodofdifferentialinequalities[1--'].Inthispaperweconsiderthecaseoffi.:(0,y,y')=0anduseaclassofnewboundarylayerfunctions.TheoremAssumethat(a)fi(x,y,z)Hfi(x,yi,'',yn,if)''jz.)eC'{xE[~l,1],yie[di,ei],ifER}andtherearepositivenondecreasingcontinuousfunctionsif,i=1,2,'…     

H~1 SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC SYSTEMS

1IntroductionInthispapertweconsiderthefollowingsystemswithinitialvaluewhereu=(tLt,'',Wi),F=(FI,'.',Fn),t20,--co0,thereisasolutionu(x,f)of(1.1),suchthatIIullHI5C(T).C(T)isaconstantdependingboundlyon"o(z)andT.Ifb=0,then(1.l)isthetypicalselnilinearheatsystems,i.e.therearemugpapersdealingwiththesystems(1.3).Theinvestigationill…     

SELF-SIMILAR SOLUTIONS OF A CLASS OF NONLINEAR PAPTIAL DIFFERENTIAL EQUATION

1IntroductionInthispaper,westudythefollowingnonlinearpartialdeferentialequationwherea(20)andp(>1)areconstants.(z,Vu(t,x))isthescalarOfxandVu(f,x),i.e.nx=(xl,...tx.),y=(yi,'',ye)then(x,y)=Zfiji.Withoutlossofgenerality,wetarei=1a=1.Thepurposeofthispaperistwo-fold.Firstweprovetheealltenceofglobalsolutions(Theorem2.1),thenweshowthatthereedestsapositivesolutionwithzeroinitialvalueinW','(Theorem1.1),thusthenon-uniquenessisestablishedwhentheinitialvalueiszeroinWI,a(R").Theorem1.1canberegardedas…     

Existence and Uniqueness of Solutions for a Class of Reaction-diffusion Systems

61.Intr0ducti0nInthispaper,wediscussareactionnetinacombusti0nmodel:V={R,,R2},whereR,andR2aredistinctreacti0nprocesses:Rl:A1+A,-A,,R2:A2+A3-P,A,(j=1,2,3)denotesthereactant,andPdenotestheinertproduct.Thesereactionsareexothermicreactions-LetQ,,Q2standforheatenergiesandU=(U,,U,,U,,U,)forstatevariablesdescribingreactions,whereUoisreactiontemporature,andU,(j=1,2,3)isthemolarityofthej-threactant.AssumethatV,(i=1,2)isthereactantvariablefortheithreactionpr0cess:V,=(Q,,1,-l,l)",V2=(Q,,O,-l,-…     

Influence asymptotique de la correction par la moyenne sur l'estimation d'un modèle AR(1) périodique

This Note studies asymptotic influence of mean-correction on the parameter least squares estimation for a periodic AR(1) model. Unlike the stationary ARMA case, we show that fitting a periodic ARMA model with intercepts to the observed series can provide substantial gains in terms of asymptotic accuracy for the parameter least squares estimators compared with fitting a periodic ARMA model without intercepts to the mean-corrected series. To cite this article: A. Gautier, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Inference in binomial AR(1) models

This paper studies inference methods for stationary time series with binomial distributions. Such series describe, for example, the number of rainy days in consecutive weeks. First, we formulate the renewal sequence version of the model that seemingly generates a new class of stationary binomial series. The model is shown to obey an AR(1) recursion in cases where the renewal lifetime has a constant hazard rate past lag one. Explicit asymptotic variances of the parameter estimators in the AR(1) case are derived from conditional least squares methods; likelihood techniques are also considered.     

Parameter estimation of hidden periodic model in random fields

Two-dimensional hidden periodic model is an important model in random fields. The model is used in the field of two-dimensional signal processing, prediction and spectral analysis. A method of estimating the parameters for the model is designed. The strong consistency of the estimators is proved. Project supported by the National Natural Science Foundation of China (Grant No. 19571002).     

灰色时序组合模型及其在地下水埋深预测中的应用

地下水埋深的变化过程是一个复杂的非线性过程,这种具有复杂的非线性组合特征的序列,使用某一种模型进行预测,结果往往不理想.在分析了灰色GM(1,1)模型、灰色GM(1,1)周期性修正模型和时序AR(n)模型的优点和缺点基础上,提出了一种新的灰色时序组合预报模型.该方法利用了GM预测所需原始数据少、方法简单的优点,用周期修正方法反映其地下水位埋深周期性波动的特征,用AR(n)模型预报其地下水位埋深的随机变化.实例研究表明,这种方法方便简洁实用且预测结果接近于实际观测值,为其它地区的地下水位埋深和相关时间序列的分析研究提供参考与借鉴作用.     

Autoregressive frequency detection using Regularized Least Squares

Tracking of an unknown frequency embedded in noise is widely applied in a variety of applications. Unknown frequencies can be obtained by approximating generalized spectral density of a periodic process by an autoregressive (AR) model. The advantage is that an AR model has a simple structure and its parameters can be easily estimated iteratively, which is crucial for online (real-time) applications. Typically, the order of the AR approximation is chosen by information criteria. However, with an increase of a sample size, model order may change, which leads to re-estimation of all model parameters. We propose a new iterative procedure for frequency detection based on a regularization of an empirical information matrix. The suggested method enables to avoid the repeated model selection as well as parameter estimation steps and therefore optimize computational costs. The asymptotic properties of the proposed regularized AR (RAR) frequency estimates are derived and performance of RAR is evaluated by numerical examples.     

基于双AR(p)模型的股价分析及其实证研究

在双AR(p)模型的基础上,选取了具有代表性的沪深300指数,并对其部分股市收盘价序列进行了平稳化处理,研究了近期中国股市的股价波动.在双.AR(p)模型严平稳条件下进行了模型诊断,最后通过动态预测得出双AR(p)模型可用于股价预测的结论.     

Asymptotic results for polygonal processes related to an autoregression

We establish functional central limit theorems for polygonal process constructed from consecutive estimators of a simple AR(1) model. We consider both stationary and unit root cases. The results are applied to change segment analysis.     

The Application of Kernel Smoothing to Time Series Data

There are already a lot of models to fit a set of stationary time series, such as AR, MA, and ARMA models. For the non-stationary data, an ARIMA or seasonal ARIMA models can be used to fit the given data. Moreover, there are also many statistical softwares that can be used to build a stationary or non-stationary time series model for a given set of time series data, such as SAS, SPLUS, etc. However, some statistical softwares wouldn＇t work well for small samples with or without missing data, especially for small time series data with seasonal trend. A nonparametric smoothing technique to build a forecasting model for a given small seasonal time series data is carried out in this paper. And then, both the method provided in this paper and that in SAS package are applied to the modeling of international airline passengers data respectively, the comparisons between the two methods are done afterwards. The results of the comparison show us the method provided in this paper has superiority over SAS＇s method.     

NONMRAMETRIC IDENTIFICATION FOR NONLINEAR AUTOREGRESSIVE TIME SERIES MODELS: CONVERGENCE RATES

61.IntroductionConsideranonlinearautoregressive(AR)modelintheformXt~f(Xt~1,'')Xt~.) st,(1.1)wheref'RP-RIisanunknownBorelfunctiononReand{s,}isani.i.d.whitenoisewithEat=0,Ear=aZ相似文献   

Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential

Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross–Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap solitons by analytical expressions involving hyperbolic functions. We justify the use of the 1D stationary coupled-mode system for a relevant elliptic problem by employing the method of Lyapunov–Schmidt reductions in Fourier space. In particular, existence of periodic/anti-periodic and decaying solutions is proved and the error terms are controlled in suitable norms. The use of multi-dimensional stationary coupled-mode systems is justified for analysis of bifurcations of periodic/anti-periodic solutions in a small multi-dimensional periodic potential.