Attraction in Numerical Minimization : Iteration Mappings, Attractors, and Basins of Attraction /: Iteration Mappings, Attractors, and Basins of Attraction. (2018)

• Record Type: Book
• Further Information: Note: Adam B. Levy.
• Other Names: Levy, Adam B
• Contents: Intro; Preface; Contents; 1 Multisets and Multiset Mappings; 1.1 Pre-distance Functions; 1.2 Calmness; 1.2.1 Calmness for Set-Valued Mappings; 1.3 Derivative Characterization of Calmness; 2 Iteration Mappings; 2.1 Coordinate-Search; 2.1.1 Iteration Mapping ICS, f; 2.2 Steepest-Descent; 2.2.1 Iteration Mapping ISDi, f; 2.3 Nelder-Mead; 2.3.1 Iteration Mapping INM, f; 2.4 Practical Considerations; 2.5 Convergence Theorems for Iteration Mappings; 3 Equilibria in Dynamical Systems; 3.1 Basins of Attraction; 3.1.1 Basin Size; 3.1.2 Basin Entropy; 3.2 Stability; 3.3 Equilibria as Minimizers 4 Attractors4.1 Local Dense Viability; 4.2 Basins of Attraction; 4.3 Stability; 4.4 Minvalue-Monotonicity; 4.5 Attractors as Minimizers; 5 Basin Analysis via Simulation; 5.1 Example 1: Two Global Minimizers; 5.1.1 Simulated Basins; 5.1.2 Basin Sizes; 5.1.3 Basin Entropy; 5.2 Example 2: One Global Minimizer and a Saddle Point; 5.2.1 Simulated Basins; 5.2.2 Basin Sizes; 5.2.3 Basin Entropy; 5.3 Example 3: One Global Minimizer and One Local Minimizer; 5.3.1 Simulated Basins; 5.3.2 Basin Sizes; 5.3.3 Basin Entropy; 5.4 Example 4: One Global Minimizer and a Ring of Local Minimizers 5.4.1 Simulated Basins5.4.2 Basin Sizes; 5.4.3 Basin Entropy; 5.5 Nelder-Mead Method; 5.5.1 Simulated Basins; 5.5.2 Basin Sizes; 5.5.3 Basin Entropy; 5.6 Practical Significance of Counterexamples; 5.6.1 Coordinate-Search and the Canoe Function; 5.6.2 The Nelder-Mead Method and McKinnon's Function; References
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 519.5; Mathematical statistics -- Data processing; Numerical analysis; MATHEMATICS / Applied; MATHEMATICS / Probability & Statistics / General; Mathematical statistics -- Data processing; Numerical analysis; Electronic books
• Languages: English
• ISBNs: 9783030040499; 3030040496
• Related ISBNs: 9783030040482
• Notes: Note: Online resource; title from PDF file page (EBSCO, viewed December 11, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.