17,187 research outputs found
The Singer of Tibet: Shabkar (1781-1851), the âInescapable Nation,â and Buddhist Universalism
This paper examines the concept of âTibet (Tib. bod)â in the spiritual autobiography of the celebrated Tibetan Buddhist author, Shabkar Tsokdruk Rangdröl (1781â1851). I use both literal and literary modes of analysis in conjunction with Steven Grosbyâs and Lama Jabbâs definitions of ânationâ to demonstrate how Shabkar initially builds a vivid personaâ the âSinger of Tibetââthat is rooted in the Tibetan landscape, but then shifts to a different personaâ âShabkarââthat transcends Tibet altogether and embraces a sense of Buddhist universalism. Throughout the process, Shabkar evokes deities and historical figures that are fundamental to Tibetan historical, cultural, and religious memory and alludes to customs and tropes central to Tibetan culture, such as orality, song, and the bardic tradition. In addition to demonstrating the efficacy and potency of literary tropes in creating the sense of an imagined nation, this essay makes a contribution to the âWhere is Tibet?â debate by exploring how Tibetan identity is articulated in one of the great masterpieces of classical Tibetan Buddhist literature
Accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes
The von Neumann-Halperin method of alternating projections converges strongly
to the projection of a given point onto the intersection of finitely many
closed affine subspaces. We propose acceleration schemes making use of two
ideas: Firstly, each projection onto an affine subspace identifies a hyperplane
of codimension 1 containing the intersection, and secondly, it is easy to
project onto a finite intersection of such hyperplanes. We give conditions for
which our accelerations converge strongly. Finally, we perform numerical
experiments to show that these accelerations perform well for a matrix model
updating problem.Comment: 16 pages, 3 figures (Corrected minor typos in Remark 2.2, Algorithm
2.5, proof of Theorem 3.12, as well as elaborated on certain proof
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