CAJ | 학술논문

随机泛函微分方程模型对大规模海量数据集的处理和训练上,有其独特的优势,解决随机泛函微分方程的边值问题,并进行收敛性分析,具有重要的意义.通过数学推导证明了半正定最小正特征带状稀疏条件下的稳定特性,对随机泛函的连续边值就行稳定误差逼近分析,采用共轭梯度法进行奇异分解,将边值收敛条件代入随机泛函椭圆函数,得到一个自回归线性最优解集,根据多目标优化理论,构建随机泛函微分方程扰动夹逼定理,根据复值函数凸组合优化定理,给定刚度矩阵小的半正定最小特征,求得该类随机泛函微分方程的边值凸组合模型渐进收敛条件.研究理论将在位移逼近和稳定性控制等领域具有较好的应用价值.
수궤범함미분방정모형대대규모해량수거집적처리화훈련상,유기독특적우세,해결수궤범함미분방정적변치문제,병진행수렴성분석,구유중요적의의.통과수학추도증명료반정정최소정특정대상희소조건하적은정특성,대수궤범함적련속변치취행은정오차핍근분석,채용공액제도법진행기이분해,장변치수렴조건대입수궤범함타원함수,득도일개자회귀선성최우해집,근거다목표우화이론,구건수궤범함미분방정우동협핍정리,근거복치함수철조합우화정리,급정강도구진소적반정정최소특정,구득해류수궤범함미분방정적변치철조합모형점진수렴조건.연구이론장재위이핍근화은정성공제등영역구유교호적응용개치.
Treatment and training of stochastic functional differential equation model for large-scale data set, has its unique advantages, solve the stochastic functional differential equation boundary value problem, and the convergence analysis, has the vital significance. Stability properties of positive semidefinite minimum positive characteristic zonal sparse conditions is proved by mathematical deduction, the line approximation error continuous edge stability analysis for stochastic functional value, singular decomposition by conjugate gradient method, the boundary conditions are incorporated into the convergence of stochastic functional elliptic function, get an autoregressive linear optimal solution set, according to the theory of multi objective optimization, construction of Stochastic Functional Differential Equations with perturbation sandwich theorem, based on complex valued function convex combination optimization theorem, given the stiffness matrix of small positive semidefinite minimum feature, convex combination model to obtain the asymptotic convergence condition of Stochastic Functional Differential Equations with boundary value. Research on the theory will have good application value in the fields of displacement approximation and stability control.