Title: Krylov Subspace Methods - Analysis and Application Author: Tomáš Gergelits Department: Department of Numerical Mathematics Supervisor: prof. Ing. Zdeněk Strakoš, DrSc., Department of Numerical Mathematics Abstract: Convergence behavior of Krylov subspace methods is often studied for linear algebraic systems with symmetric positive definite matrices in terms of the condition number of the system matrix. As recalled in the first part of this thesis, their actual convergence behavior (that can be in practice also substantially affected by rounding errors) is however determined by the whole spectrum of the system matrix, and by the projections of the initial residual to the associated invariant subspaces. The core part of this thesis investigates the spectra of infinite dimensional operators −∇ · (k(x)∇) and −∇ · (K(x)∇), where k(x) is a scalar coefficient function and K(x) is a symmetric tensor function, preconditioned by the Laplace operator. Subsequently, the focus is on the eigenvalues of the matrices that arise from the discretization using conforming finite elements. Assuming continuity of K(x), it is proved that the spectrum of the preconditi- oned infinite dimensional operator is equal to the convex hull of the ranges of the diagonal function entries of Λ(x) from the spectral decomposition K(x) =...

從目前數位家庭產業的相關研究與發展中，本研究以廠商業者與消費者的角度探討對數位家庭的看法，整理各先進國家在數位家庭產業的發展，以及各個大廠的數位家庭發展策略。 本研究認為目前數位家庭產業以數位內容業者，數位服務加值廠商，網路與電信業者，以及資通訊與消費性電子產品廠商為核心，仍處於一起始階段，無明顯主導廠商；此外，光纖到府之高普及率、高度整合與互連性的數位設備、豐富且有價值的數位內容以及從消費者為出發點容易使用的數位家庭應用是為數位家庭產業成功關鍵因素。 另一方面，因應數位家庭的趨勢潮流，台灣除了參考美日韓等國的數位家庭相關政策與法令外，在產業策略面，必須利用台灣既有的優勢，除了為國內高科技電子產業找出下一階段的出路，更要積極累積異業整合的經驗，並以全球華人為目標，發展數位內容與服務。 / Involving in recent industry researches of digital home, the study has elaborated the development strategies of digital home industry in some advanced countries and manufacturers. The study tried to clear the digital home’s situation either from manufacturers’ or consumers’ opinions. Digital content providers, value-added service providers, ISP, and 3C manufacturers are seen as core roles in the development of digital home industry. However, who is the leader is not yet clear. In addition, the study showed that the popularization of FTTH, digital equipments with high integration, colorful digital contents, and all kinds of related digital applications should be designed from consumers’ concern are the key success factors in the digital home industry. Under the development trend of digital home industry, besides referencing related country strategies of America, Japan, and Korea, Taiwan government should take advantage of company’s superiorities well to help high-tech electronics companies find out their ways in the future. Furthermore, manufacturers in Taiwan should actively accumulate across-industry integrated experiences, and focus market on the Chinese people to develop all kinds of digital contents and service.