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Can I read Optimal Location on a Sphere on EtoBox?
Optimal Location on a Sphere by I. Norman Katz; Leon Cooper is a Engineering article available to read on EtoBox.
What is Optimal Location on a Sphere about?
The problem of finding a point on the sphere Sz = {a = (x, y, z) Ix2 + y\* t z\* = l} which minimizes the weighted sum of the distances to N given destination points 4 on S\* is studied. Three different metrics are considered as distances between points on S': (A), square of Euclidean distance; (B), Euclidean distance; (C), great circle distance. Non uniqueness of minimizers is demonstrated and some pathological cases are studied. An algorithm, analogous to the Weiszfeld algorithm for the classical unconstrained Weber problem is formulated, and its convergence properties are investigated. A necessary and sufficient condition for a destination point to be a local minimizer is derived. Finally, a modified form of Steffensen's acceleration is given and the results of numerical tests are presented. These results illustrate the predictions of the theory, and confirm the effectiveness of Steffensen's acceleration.
Who reads Optimal Location on a Sphere?
It is typically read by researchers, students, and practitioners in Engineering.
- Author
- I. Norman Katz; Leon Cooper
- Publisher
- Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0898-1221)
- Published
- 1980
- Language
- EN
- Field
- Engineering (Physical Sciences)