An adaptive sparse polynomial dimensional decomposition based on Bayesian compressive sensing and cross-entropy

He, Wanxin; Li, Gang; Nie, Zhaokun

doi:10.1007/s00158-021-03120-w

Cited by 7 publications

(1 citation statement)

References 61 publications

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“…The polynomial order signifies the fine details of the signal represented by the polynomial. On the other hand, the size of the orthogonal polynomials indicates the total number of polynomials in a given set of orthogonal polynomials [27,28]. Note that the higher the order, the more accurate the representation of the signal in the transform domain [29].…”

Section: Introductionmentioning

confidence: 99%

High-Performance Krawtchouk Polynomials of High Order Based on Multithreading

Flayyih,

Al-sudani,

Mahmmod

et al. 2024

Computation

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Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parallel processing capabilities of modern central processing units (CPUs), namely the availability of multiple cores and multithreading. The proposed multi-threaded implementations for computing DKraP coefficients divide the computations into multiple independent tasks, which are executed concurrently by different threads distributed among the independent cores. This multi-threaded approach has been evaluated across a range of DKraP sizes and various values of polynomial parameters. The results show that the proposed method achieves a significant reduction in computation time. In addition, the proposed method has the added benefit of applying to larger polynomial sizes and a wider range of Krawtchouk polynomial parameters. Furthermore, an accurate and appropriate selection scheme of the recurrence algorithm is introduced. The proposed approach introduced in this paper makes the DKraP coefficient computation an attractive solution for a variety of applications.

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Section: Introductionmentioning

confidence: 99%