The sign function of a square matrix was introduced by Roberts in 1971. We show that it is useful to regard S = sign(A) as being part of a matrix sign decomposition A = SN, where N = (A ) ’ 1/z This decomposition leads to . the new representation sign(A) = A(A2)-‘i2. Most results for the matrix sign decomposition have a counterpart for the polar decomposition A = UH, and vice versa. To illustra...

Objective (s): Various iterative reconstruction algorithms in nuclear medicine have been introduced in the last three decades. For each new imaging system, it is wise to select appropriate image reconstruction algorithms and evaluate their performance. In this study, three approaches of image reconstruction were developed for a novel desktop open-gantry SPECT system, PERSPECT, to assess their p...

This appendix contains the proof of Theorem 2 which is the main result for the general version of the model presented in Section II of the paper. The numbering here (of equations, result, and definitions, etc.) follows the numbering in the published paper. Assumptions 6-10, which are stated in the paper, are assumed implicitly throughout. A single subscript will be used to denote the number of ...

We consider approximation of diameter of a set S of n points in dimension m. Eg̃eciog̃lu and Kalantari [8] have shown that given any p ∈ S, by computing its farthest in S, say q, and in turn the farthest point of q, say q′, we have diam(S) ≤ √ 3 d(q, q′). Furthermore, iteratively replacing p with an appropriately selected point on the line segment pq, in at most t ≤ n additional iterations, the c...

Perennial iterations of Olympic Games, and the International Committee’s (IOC) contractual obligations upon host cities, have prompted development wide-ranging educational initiatives. S...