Topic
Meyer wavelet
About: Meyer wavelet is a research topic. Over the lifetime, 223 publications have been published within this topic receiving 2956 citations.
Papers published on a yearly basis
Papers
TL;DR: Average case and probabilistic settings are considered and it turns out that in these two settings, worst case unsolvable or intractable problems become solvable or tractable.
Abstract: analyzed. Roughly speaking, when the residual criterion is used, the error of an approximate solution is measured by how much it violates the equation rather than by its distance from the true solution. The worst case setting is the most reassuring setting since the cost and errors of algorithms are defined by their worst case performance. However, for some problems it is too pessimistic and it causes the respective worst case complexity to be huge. This is especially the case for multivariate problems. For ill-posed problems, the situation is even worse since the worst case complexity is infinite. To cope with such intractability (or unsolvability) analyzing the problems in other settings is in order. Therefore, in Chapter 7, average case and probabilistic settings are considered. In these settings, the space of functions is equipped with a probability measure (Gaussian measures are assumed through out the book). Then the error and cost of algorithms are measured by their expectations (average case setting) or probability of being too large (probabilistic setting) instead of by their maximal values. It turns out that in these two settings, worst case unsolvable or intractable problems become solvable or tractable. Another two settings, asymptotic and randomized, are considered in Chapter 8. Both settings are closely related to the worst case setting; however, in the asymptotic setting sequences of algorithms with increasing number of information pieces are studied. A winner is the one with the fastest rate of convergence. In the randomized setting, nondeterministic (random) information and algorithms (e.g., Monte Carlo methods) are allowed. am not quoting concrete results on complexities for various problems and/or settings; in particular, how much complexity reduction is gained by switching from the worst case setting to other settings. Doing so would be like telling the conclusion of a suspense novel to the reader who is about to start reading it. Hence, instead, let me strongly recommend this valuable book.
223 citations
TL;DR: In this paper, bearing defect is detected using the stator current analysis via Meyer wavelet in the wavelet packet structure, with energy comparison as the fault index, and the presented method is evaluated using experimental signals.
202 citations
TL;DR: The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures, and the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver.
Abstract: In the present study, a novel fractional Meyer neuro-evolution-based intelligent computing solver (FMNEICS) is presented for numerical treatment of doubly singular multi-fractional Lane–Emden system (DSMF-LES) using combined heuristics of Meyer wavelet neural networks (MWNN) optimized with global search efficacy of genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., MWNN-GASQP. The design of novel FMNEICS for DSMF-LES is presented after derivation from standard Lane–Emden equation, and the singular points and shape factors along with fractional-order terms are analyzed. The MWNN modeling strength is used to represent the system model DSMF-LES in the mean-squared error-based merit function and optimization of the networks is carried out with integrated optimization ability of GASQP. The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures. Moreover, the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver.
101 citations
TL;DR: In this paper, it was shown that when the same procedure is applied to biorthogonal wavelet bases, not all the resulting wavelet packets lead to Riesz bases for a factor of O(L 2 (L √ 2 (log n) ).
Abstract: Starting from a multiresolution analysis and the corresponding orthonormal wavelet basis, Coifman and Meyer have constructed wavelet packets, a library from which many different orthonormal bases can be picked. This paper proves that when the same procedure is applied to biorthogonal wavelet bases, not all the resulting wavelet packets lead to Riesz bases for $L^2 (\mathbb{R})$.
88 citations
TL;DR: In this article, the notion of orthonormal wavelet packets introduced by Coifman and Meyer is generalized to the nonorthogonal setting in order to include compactly supported and symmetric basis functions.
Abstract: The notion of orthonormal wavelet packets introduced by Coifman and Meyer is generalized to the nonorthogonal setting in order to include compactly supported and symmetric basis functions. In particular, dual (or biorthogonal) wavelet packets are investigated and a stability result is established. Algorithms for implementations are also developed.
77 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 9 |
| 2020 | 4 |
| 2019 | 7 |
| 2018 | 8 |
| 2017 | 9 |
| 2016 | 12 |