The Singer of Tibet: Shabkar (1781-1851), the “Inescapable Nation,” and Buddhist Universalism

This paper examines the concept of ‘Tibet (Tib. bod)’ in the spiritual autobiography of the celebrated Tibetan Buddhist author, Shabkar Tsokdruk Rangdröl (1781–1851). I use both literal and literary modes of analysis in conjunction with Steven Grosby’s and Lama Jabb’s definitions of ‘nation’ to demonstrate how Shabkar initially builds a vivid persona— the ‘Singer of Tibet’—that is rooted in the Tibetan landscape, but then shifts to a different persona— ‘Shabkar’—that 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 ‘Where is Tibet?’ 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