Applied Numerical Mathematics最新文献

{"title":"Fractal properties of 4-point interpolatory subdivision schemes and wavelet scattering transform for signal classification","authors":"V. Bruni ,&nbsp;F. Pelosi ,&nbsp;D. Vitulano","doi":"10.1016/j.apnum.2024.09.022","DOIUrl":"10.1016/j.apnum.2024.09.022","url":null,"abstract":"<div><div>Wavelet scattering is a recent time-frequency transform that shares the convolutional architecture with convolutional neural networks, but it allows for a faster training and it often requires smaller training sets. It consists of a multistage non-linear transform that allows us to compute the deep spectrum of a signal by cascading convolution, non-linear operator and pooling at each stage, resulting a powerful tool for signal classification when embedded in machine learning architectures. One of the most delicate parameters in convolutional architectures is the temporal sampling that strongly affects the computational load as well as the classification rate. In this paper the role of sampling in the wavelet scattering transform is studied for signal classification purposes. In particular, the role of subdivision schemes in properly compensating the information lost when using sampling at each stage of the transform is investigated. Preliminary experimental results show that, starting from coarse grids, interpolatory subdivision schemes reproduce copies of the original scattering coefficients at a fixed full grid that still represent distinctive features for signal classes. In fact, thanks to the ability of the scheme in reproducing similar fractal properties of the transform through an efficient iterative refinement procedure, the reproduced coefficients enable to obtain classification rates similar to those provided by the native wavelet scattering transform. The relationships between the tension parameter of the scheme and the fractal dimension of its limit curve are also investigated.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 256-270"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical solution of the forward Kolmogorov equations in population genetics using Eta functions","authors":"Somayeh Mashayekhi ,&nbsp;Salameh Sedaghat","doi":"10.1016/j.apnum.2024.10.013","DOIUrl":"10.1016/j.apnum.2024.10.013","url":null,"abstract":"<div><div>This paper introduces a new numerical method for solving forward Kolmogorov equations in population genetics. Since there's no simple analytical expression for the distribution of allele frequencies (DAF), we use these equations to derive it. The accuracy of solving these equations depends on the choice of base functions, so we use Eta-based functions for better approximations. By employing the operational matrix of integral, we simplify the partial differential equation to an algebraic one. The method's error bounds, stability, and validity are demonstrated through numerical examples. Finally, we apply this method to analyze the behavior of forward Kolmogorov equations under various evolutionary forces.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 160-175"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamics of thermoviscoelastic solids of grade 3","authors":"Vito Antonio Cimmelli","doi":"10.1016/j.apnum.2024.10.014","DOIUrl":"10.1016/j.apnum.2024.10.014","url":null,"abstract":"<div><div>A generalized Coleman-Noll procedure is applied to analyze thermoviscoelastic solids of grade 3, namely, solids with constitutive equations depending on the third spatial gradient of the deformation. Some new forms of stress tensor and specific entropy are obtained. For small deformations, the equilibrium problem is studied for onedimensional systems. An explicit form of the displacement is calculated. A comparison with the equilibrium theory of Korteweg fluids is carried out.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 301-313"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient algorithms of box-constrained Nonnegative Matrix Factorization and its applications in image clustering","authors":"Jie Guo ,&nbsp;Ting Li ,&nbsp;Zhong Wan ,&nbsp;Jiaoyan Li ,&nbsp;Yamei Xiao","doi":"10.1016/j.apnum.2024.10.015","DOIUrl":"10.1016/j.apnum.2024.10.015","url":null,"abstract":"<div><div>Nonnegative Matrix Factorization (NMF) provides an important approach of unsupervising learning, but it faces computational challenges when applied into clustering of high-dimensional datasets. In this paper, a class of novel nonmonotone gradient-descent algorithms are developed for solving box-constrained NMF problems. Unlike existing algorithms in the literature that update each matrix factor individually by fixing another one, our algorithms simultaneously update the paired matrix factors by leveraging adaptive projected Barzilai-Borwein directions and appropriate step sizes generated by the developed nonmonotone line search rules. Theoretically, it is proved that the developed algorithms are well defined and globally convergent. Extensive numerical tests on public image datasets demonstrate that the developed algorithms in this paper outperform the state-of-the-art ones, in terms of clustering performance, computational efficiency, and robustness of mining noisy data.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 176-188"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical methods in modeling with supersaturated designs","authors":"N. Koukoudakis ,&nbsp;C. Koukouvinos ,&nbsp;A. Lappa ,&nbsp;M. Mitrouli ,&nbsp;A. Psitou","doi":"10.1016/j.apnum.2024.02.003","DOIUrl":"10.1016/j.apnum.2024.02.003","url":null,"abstract":"<div><div>The present study aims to investigate the application of several numerical methods<span><span> in least square problems, when the </span>design matrix<span> is a supersaturated design. This kind of statistical modeling appears frequently in a majority of applications and experiments where the main scope concerns the identification of the appropriate active factors and possible interactions as well. Several real data sets are analyzed and useful remarks and comparisons concerning the selection of the most appropriate factors are presented.</span></span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 271-283"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139814933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sparse approximation of complex networks","authors":"Omar De la Cruz Cabrera,&nbsp;Jiafeng Jin,&nbsp;Lothar Reichel","doi":"10.1016/j.apnum.2024.01.002","DOIUrl":"10.1016/j.apnum.2024.01.002","url":null,"abstract":"<div><div><span>This paper considers the problem of recovering a sparse approximation </span><span><math><mi>A</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msup></math></span><span> of an unknown (exact) adjacency matrix </span><span><math><msub><mrow><mi>A</mi></mrow><mrow><mtext>true</mtext></mrow></msub></math></span> for a network from a corrupted version of a communicability matrix <span><math><mi>C</mi><mo>=</mo><mi>exp</mi><mo>⁡</mo><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mtext>true</mtext></mrow></msub><mo>)</mo><mo>+</mo><mi>N</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msup></math></span>, where <strong>N</strong> denotes an unknown “noise matrix”. We consider two methods for determining an approximation <strong>A</strong> of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mtext>true</mtext></mrow></msub></math></span>: <span><math><mo>(</mo><mrow><mi>i</mi><mo>)</mo></mrow></math></span><span> a Newton method with soft-thresholding and line search, and </span><span><math><mo>(</mo><mrow><mi>ii</mi><mo>)</mo></mrow></math></span><span> a proximal gradient method with line search. These methods are applied to compute the solution of the minimization problem</span><span><span><span><math><munder><mrow><mi>arg</mi><mo>⁡</mo><mi>min</mi></mrow><mrow><mi>A</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msup></mrow></munder><mo>{</mo><msubsup><mrow><mo>‖</mo><mi>exp</mi><mo>⁡</mo><mo>(</mo><mi>A</mi><mo>)</mo><mo>−</mo><mi>C</mi><mo>‖</mo></mrow><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><mi>μ</mi><msub><mrow><mo>‖</mo><mtext>vec</mtext><mo>(</mo><mi>A</mi><mo>)</mo><mo>‖</mo></mrow><mrow><mn>1</mn></mrow></msub><mo>}</mo><mo>,</mo></math></span></span></span> where <span><math><mi>μ</mi><mo>&gt;</mo><mn>0</mn></math></span><span> is a regularization parameter that controls the amount of shrinkage. We discuss the effect of </span><em>μ</em><span> on the computed solution, conditions for convergence, and the rate of convergence of the methods. Computed examples illustrate their performance when applied to directed and undirected networks.</span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 170-188"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical modelling of problems with delay and after-effect","authors":"Neville J. Ford","doi":"10.1016/j.apnum.2024.10.007","DOIUrl":"10.1016/j.apnum.2024.10.007","url":null,"abstract":"<div><div>This paper provides a tutorial review of the use of delay differential equations in mathematical models of real problems. We use the COVID-19 pandemic as an example to help explain our conclusions. We present the fundamental delay differential equation as a prototype for modelling problems where there is a delay or after-effect, and we reveal (via the characteristic values) the infinite dimensional nature of the equation and the presence of oscillatory solutions not seen in corresponding equations without delay. We discuss how models were constructed for the COVID-19 pandemic, particularly in view of the relative lack of understanding of the disease and the paucity of available data in the early stages, and we identify both strengths and weaknesses in the modelling predictions and how they were communicated and applied. We consider the question of whether equations with delay could have been or should have been utilised at various stages in order to make more accurate or more useful predictions.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 338-347"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical solutions of stochastic delay integro-differential equations by block pulse functions","authors":"Guo Jiang,&nbsp;Yuanqin Chen,&nbsp;Jiayi Ying","doi":"10.1016/j.apnum.2024.10.017","DOIUrl":"10.1016/j.apnum.2024.10.017","url":null,"abstract":"<div><div>This paper presents an efficient numerical method for solving nonlinear stochastic delay integro-differential equations based on block pulse functions. Firstly, the equation is transformed into an algebraic system by the integral delay operator matrixes of block pulse functions. Then, error analysis is conducted on the method. Finally, some numerical examples are provided to validate the method. This work provides numerical solutions for the stochastic delay integro-differential equations by global approximation method. This method has the advantages of simple calculation and higher error accuracy.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 214-230"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A rank-updating technique for the Kronecker canonical form of singular pencils","authors":"Dimitrios Christou ,&nbsp;Marilena Mitrouli ,&nbsp;Dimitrios Triantafyllou","doi":"10.1016/j.apnum.2024.01.015","DOIUrl":"10.1016/j.apnum.2024.01.015","url":null,"abstract":"<div><div>For a linear time-invariant system <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>A</mi><mi>x</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><mi>B</mi><mi>u</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span><span>, the Kronecker canonical form<span> (KCF) of the matrix pencil </span></span><span><math><mo>(</mo><mi>s</mi><mi>I</mi><mo>−</mo><mi>A</mi><mspace></mspace><mo>|</mo><mspace></mspace><mi>B</mi><mo>)</mo></math></span><span> provides the controllability indices, also called column minimal indices, of the system and their sum corresponds to the dimension of the controllable subspace. In this paper we introduce a fast numerical algorithm for computing the sets of column/row minimal indices of a singular pencil </span><span><math><mi>s</mi><mi>F</mi><mo>−</mo><mi>G</mi></math></span><span> using a rank-updating technique and the properties of piecewise arithmetic progression sequences defined by the size of the null spaces of appropriate Toeplitz matrices. The method is demonstrated and tested on various data sets.</span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 135-145"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139557855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solving the two-dimensional time-dependent Schrödinger equation using the Sinc collocation method and double exponential transformations","authors":"S. Elgharbi ,&nbsp;M. Essaouini ,&nbsp;B. Abouzaid ,&nbsp;H. Safouhi","doi":"10.1016/j.apnum.2024.04.002","DOIUrl":"10.1016/j.apnum.2024.04.002","url":null,"abstract":"<div><div>Over the last four decades, Sinc methods have occupied an important place in numerical analysis due to their simplicity and great performance. An incorporation of the Sinc collocation method with double exponential transformation is used to solve the two-dimensional time dependent Schrödinger equation. Numerical comparison between the double exponential and single exponential approaches is made to illustrate the superiority of the double exponential Sinc method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 222-231"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140772854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}