Properties of Generalized Polynomial Spaces in Three Variables

2009 ◽  
pp. 509-516
Author(s):  
Dana Simian
Keyword(s):  
Generalized Polynomial

scholarly journals Fast and Generalized Polynomial Time Memory Consistency Verification

2006 ◽  
pp. 503-516 ◽  
Author(s):  
Amitabha Roy ◽  
Stephan Zeisset ◽  
Charles J. Fleckenstein ◽  
John C. Huang
Keyword(s):  
Polynomial Time ◽  
Memory Consistency ◽  
Generalized Polynomial ◽  
Consistency Verification

On Global Feasible Search for Global Design Optimization With Application to Generalized Polynomial Models

1992 ◽  
Author(s):  
Chihsiung Lo ◽  
Panos Y. Papalambros
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Model Transformation ◽  
Special Problem ◽  
Search Algorithms ◽  
Deterministic Global Optimization ◽  
Generalized Polynomial ◽  
Polynomial Models ◽  
Feasible Solutions ◽  
Global Design Optimization

Abstract A powerful idea for deterministic global optimization is the use of global feasible search, namely, algorithms that guarantee finding feasible solutions of nonconvex problems or prove that none exists. In this article, a set of conditions for global feasible search algorithms is established. The utility of these conditions is demonstrated on two algorithms that solve special problem classes globally. Also, a new model transformation is shown to convert a generalized polynomial problem into one of the special classes above. A flywheel design example illustrates the approach. A sequel article provides further computational details and design examples.

scholarly journals Encoding through generalized polynomial codes

2011 ◽  
Vol 30 (2) ◽  
pp. 349-366 ◽  
Author(s):  
T. Shah ◽  
A. Khan ◽  
A. A. Andrade
Keyword(s):  
Generalized Polynomial ◽  
Polynomial Codes

Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs

2019 ◽  
Vol 19 (1) ◽  
pp. 39-53 ◽  
Author(s):  
Martin Eigel ◽  
Johannes Neumann ◽  
Reinhold Schneider ◽  
Sebastian Wolf
Keyword(s):  
Polynomial Chaos ◽  
Monte Carlo Sampling ◽  
Black Box ◽  
Low Rank ◽  
High Dimensional ◽  
Reconstruction Procedure ◽  
Numerical Examples ◽  
Quasi Monte Carlo ◽  
Generalized Polynomial ◽  
Stochastic Solution

AbstractThis paper examines a completely non-intrusive, sample-based method for the computation of functional low-rank solutions of high-dimensional parametric random PDEs, which have become an area of intensive research in Uncertainty Quantification (UQ). In order to obtain a generalized polynomial chaos representation of the approximate stochastic solution, a novel black-box rank-adapted tensor reconstruction procedure is proposed. The performance of the described approach is illustrated with several numerical examples and compared to (Quasi-)Monte Carlo sampling.

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