Empirical model-building and response surface
Empirical model-building and response surface
Response surfaces: designs and analyses
Response surfaces: designs and analyses
Practical numerical algorithms for chaotic systems
Practical numerical algorithms for chaotic systems
Signal representation using adaptive normalized Gaussian functions
Signal Processing
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Matlab guide
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Fast Atomic Decomposition by the Inhibition Method
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Entropy-based algorithms for best basis selection
IEEE Transactions on Information Theory - Part 2
Time-frequency localization operators: a geometric phase space approach
IEEE Transactions on Information Theory
Journal of Computational and Applied Mathematics
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We develop algorithms to find the so-called effective points (EPs) x@?X@?R^n such that the corresponding responses f(x)@?R belong to a specific region of interest (ROI). Examples of an ROI include extreme values, bounded intervals, and positivity. We are especially interested in the problem defined by the following characteristics: (i) the definition of f(x) is either complicated or implicit, (ii) the response surface f(X) does not fit simple patterns, and (iii) computational costs of function evaluations is high. To solve this problem, we iteratively approximate the true yet unknown response surface with simplified surrogate models and then use the surrogate models to predict the possible EPs. Unlike interpolation schemes, the surrogate models are formed by linear combinations of a set of overcomplete bases and they are not obliged to fit the known response value. A numerical example that involves finding positive Lyapunov exponents of a dynamical system shows that the algorithm is efficient and practical.