论文标题
对线性连续方程的统一观点在科学中普遍存在。第六部分：解决方案的快速融合系列扩展
A unifying perspective on linear continuum equations prevalent in science. Part VI: rapidly converging series expansions for their solution
论文作者
论文摘要
We obtain rapidly convergent series expansions of resolvents of operators taking the form ${\bf A}=Γ_1{\bf B}Γ_1$ where $Γ_1({\bf k})$ is a projection that acts locally in Fourier space and ${\bf B}({\bf x})$ is an operator that acts locally in real space.当人们想解决在第一部分，II，III和IV中调查的任何大型线性物理方程时，这种分解自然就会产生，这些方程可以在扩展的复合材料的抽象理论中重新构成问题。我们展示了有关$ {\ bf a} $频谱的信息如何用于大大提高收敛速率。
We obtain rapidly convergent series expansions of resolvents of operators taking the form ${\bf A}=Γ_1{\bf B}Γ_1$ where $Γ_1({\bf k})$ is a projection that acts locally in Fourier space and ${\bf B}({\bf x})$ is an operator that acts locally in real space. Such resolvents arise naturally when one wants to solve any of the large class of linear physical equations surveyed in Parts I, II, III, and IV that can be reformulated as problems in the extended abstract theory of composites. We show how the information about the spectrum of ${\bf A}$ can be used to greatly improve the convergence rate.
