Pub Date : 2024-07-24DOI: 10.11648/j.acm.20241304.12
Mervat M. A. Mahmoud, N. E. Elashker
The integer Constant Division (ICD) is the type of integer division in which the divisor is known in advance, enabling pre-computing operations to be included. Therefore, it can be more efficient regarding computing resources and time. However, most ICD techniques are restricted by a few values or narrow boundaries for the divisor. On the other hand, the main approaches of the division algorithms, where the divisor is variable, are digit-by-digit and convergence methods. The first techniques are simple and have less sophisticated conversion logic for the quotient but also have the problem of taking significantly long latency. On the contrary, the convergence techniques rely on multiplication rather than subtraction. They estimate the quotient of division providing the quotient with minimal latency at the expense of precision. This article suggests a precise, generic, and novel integer division algorithm based on sequential recursion with fewer iterations. The suggested methodology relies on extracting the division results for non-powers-of-two divisors from those for the closest power-of-two divisors, which are obtained simply using the right bit shifting. To the authors’ best knowledge of the state-of-the-art, the number of iterations in the recurrent variable division is half the divisor bit size, and the Sweeney, Robertson, and Tocher (SRT) division, which is named after its developers, involves log2(n) iterations. The suggested algorithm has an [(m/(n-1))-1] number of recursive iterations, where m and n are the number of bits of the dividend and the divisor, respectively. The design is simulated in the Vivado tool for validation and implemented with a Zynq UltraScale FPGA. The technique performance depends on the number of nested divisions and the size of a LUT. The two factors change according to the value of the divisor. Nevertheless, the size of the LUT is proportional to the range and the number of bits of the divisor. Furthermore, the equation that controls the number of nested blocks is illustrated in the manuscript. The proposed technique applies to both constant and variable divisors with a compact hardware area in the case of constant division. The hardware implementation of constant division has unlimited values for dividends and divisors with a compact hardware area in the case of large divisors. However, using the design in the hardware implementation of variable division is up to 64-bit dividend and 12-bit divisor. The result analysis demonstrates that this algorithm is more efficient for constant division for large numbers.
{"title":"Novel Integer Division for Embedded Systems: Generic Algorithm Optimal for Large Divisors","authors":"Mervat M. A. Mahmoud, N. E. Elashker","doi":"10.11648/j.acm.20241304.12","DOIUrl":"https://doi.org/10.11648/j.acm.20241304.12","url":null,"abstract":"The integer Constant Division (ICD) is the type of integer division in which the divisor is known in advance, enabling pre-computing operations to be included. Therefore, it can be more efficient regarding computing resources and time. However, most ICD techniques are restricted by a few values or narrow boundaries for the divisor. On the other hand, the main approaches of the division algorithms, where the divisor is variable, are digit-by-digit and convergence methods. The first techniques are simple and have less sophisticated conversion logic for the quotient but also have the problem of taking significantly long latency. On the contrary, the convergence techniques rely on multiplication rather than subtraction. They estimate the quotient of division providing the quotient with minimal latency at the expense of precision. This article suggests a precise, generic, and novel integer division algorithm based on sequential recursion with fewer iterations. The suggested methodology relies on extracting the division results for non-powers-of-two divisors from those for the closest power-of-two divisors, which are obtained simply using the right bit shifting. To the authors’ best knowledge of the state-of-the-art, the number of iterations in the recurrent variable division is half the divisor bit size, and the Sweeney, Robertson, and Tocher (SRT) division, which is named after its developers, involves <i>log</i><sub>2</sub>(n) iterations. The suggested algorithm has an [(m/(n-1))-1] number of recursive iterations, where m and n are the number of bits of the dividend and the divisor, respectively. The design is simulated in the Vivado tool for validation and implemented with a Zynq UltraScale FPGA. The technique performance depends on the number of nested divisions and the size of a LUT. The two factors change according to the value of the divisor. Nevertheless, the size of the LUT is proportional to the range and the number of bits of the divisor. Furthermore, the equation that controls the number of nested blocks is illustrated in the manuscript. The proposed technique applies to both constant and variable divisors with a compact hardware area in the case of constant division. The hardware implementation of constant division has unlimited values for dividends and divisors with a compact hardware area in the case of large divisors. However, using the design in the hardware implementation of variable division is up to 64-bit dividend and 12-bit divisor. The result analysis demonstrates that this algorithm is more efficient for constant division for large numbers.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":4.6,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141806553","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}
Pub Date : 2024-07-05DOI: 10.11648/j.acm.20241304.11
Mouhamadou Djima Baranon, Patrick G. O. Weke, Judicaël Alladatin, Boni Maxime Ale, A. Langat
The application of Hidden Markov Models (HMMs) in the study of genetic and neurological disorders has shown significant potential in advancing our understanding and treatment of these conditions. This review assesses 77 papers selected from a pool of 1,105 records to evaluate the use of HMMs in disease research. After the exclusion of duplicate and irrelevant records, the papers were analyzed for their focus on HMM applications and regional representation. A notable deficiency was identified in research across regions such as Africa, South America, and Oceania, emphasizing the need for more diverse and inclusive studies in these areas. Additionally, many studies did not adequately address the role of genetic mutations in the onset and progression of these diseases, revealing a critical research gap that warrants further investigation. Future research efforts should prioritize the examination of mutations to deepen our understanding of how these changes impact the development and progression of genetic and neurological disorders. By addressing these gaps, the scientific community can facilitate the development of more effective and personalized treatments, ultimately enhancing health outcomes on a global scale. Overall, this review highlights the importance of HMMs in this area of research and underscores the necessity of broadening the scope of future studies to include a wider variety of geographical regions and a more comprehensive investigation of genetic mutations.
{"title":"Exploring Hidden Markov Models in the Context of Genetic Disorders, and Related Conditions: A Systematic Review","authors":"Mouhamadou Djima Baranon, Patrick G. O. Weke, Judicaël Alladatin, Boni Maxime Ale, A. Langat","doi":"10.11648/j.acm.20241304.11","DOIUrl":"https://doi.org/10.11648/j.acm.20241304.11","url":null,"abstract":"The application of Hidden Markov Models (HMMs) in the study of genetic and neurological disorders has shown significant potential in advancing our understanding and treatment of these conditions. This review assesses 77 papers selected from a pool of 1,105 records to evaluate the use of HMMs in disease research. After the exclusion of duplicate and irrelevant records, the papers were analyzed for their focus on HMM applications and regional representation. A notable deficiency was identified in research across regions such as Africa, South America, and Oceania, emphasizing the need for more diverse and inclusive studies in these areas. Additionally, many studies did not adequately address the role of genetic mutations in the onset and progression of these diseases, revealing a critical research gap that warrants further investigation. Future research efforts should prioritize the examination of mutations to deepen our understanding of how these changes impact the development and progression of genetic and neurological disorders. By addressing these gaps, the scientific community can facilitate the development of more effective and personalized treatments, ultimately enhancing health outcomes on a global scale. Overall, this review highlights the importance of HMMs in this area of research and underscores the necessity of broadening the scope of future studies to include a wider variety of geographical regions and a more comprehensive investigation of genetic mutations.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":4.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674809","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}
Pub Date : 2024-06-03DOI: 10.11648/j.acm.20241303.12
Muhammad Islam, Muhammad Hossain
This article presents a simple efficient and asynchronously correcting a posteriori error approximation for discontinuous finite element solutions of the second-order hyperbolic partial differential problems on triangular meshes. This study considersthe basis functions for error spaces corresponding to some finite element spaces. The discretization error of each triangle is estimated by solving the local error problem. It also shows global super convergence for discontinuous solution on triangular lattice. In this article, the triangular elements are classify into three types: (i) elements with one inflow and two outflow edges are of type I, (ii) elements with two inflows and one outflow edges are of type II and (iii) elements with one inflow edge, one outflow edge, and one edge parallel to the characteristics are of type III. The article investigated higher-dimension discontinuous Galerkin methods for hyperbolic problems on triangular meshes and also studied the effect of finite element spaces on the superconvergence properties of DG solutions on three types of triangular elements and it showed that the DG solution is O(hp+2) superconvergent at Legendre points on the outflow edge on triangles having one outflow edge using three polynomial spaces. A posteriori error estimates are tested on a number of linear and nonlinear problems to show their efficiency and accuracy under lattice refinement for smooth and discontinuous solutions.
本文针对三角形网格上二阶双曲偏微分问题的非连续有限元解，提出了一种简单高效且异步修正后验误差的近似方法。本研究考虑了与某些有限元空间相对应的误差空间的基函数。通过求解局部误差问题来估计每个三角形的离散化误差。它还显示了三角形网格上不连续解的全局超收敛性。本文将三角形元素分为三类：(i) 具有一个流入边和两个流出边的元素为 I 类；(ii) 具有两个流入边和一个流出边的元素为 II 类；(iii) 具有一个流入边、一个流出边和一个平行于特征的边的元素为 III 类。文章研究了三角形网格上双曲问题的高维度非连续 Galerkin 方法，还研究了有限元空间对三种三角形元素上 DG 解的超收敛特性的影响，结果表明，在有一个流出边的三角形上，使用三个多项式空间，DG 解在流出边上的 Legendre 点具有 O(hp+2) 的超收敛性。在一些线性和非线性问题上测试了后验误差估计，以显示其在光滑和不连续解的网格细化下的效率和准确性。
{"title":"Error Approximation of the Second Order Hyperbolic Differential Equationby Using DG Finite Element Method","authors":"Muhammad Islam, Muhammad Hossain","doi":"10.11648/j.acm.20241303.12","DOIUrl":"https://doi.org/10.11648/j.acm.20241303.12","url":null,"abstract":"This article presents a simple efficient and asynchronously correcting a posteriori error approximation for discontinuous finite element solutions of the second-order hyperbolic partial differential problems on triangular meshes. This study considersthe basis functions for error spaces corresponding to some finite element spaces. The discretization error of each triangle is estimated by solving the local error problem. It also shows global super convergence for discontinuous solution on triangular lattice. In this article, the triangular elements are classify into three types: (i) elements with one inflow and two outflow edges are of type I, (ii) elements with two inflows and one outflow edges are of type II and (iii) elements with one inflow edge, one outflow edge, and one edge parallel to the characteristics are of type III. The article investigated higher-dimension discontinuous Galerkin methods for hyperbolic problems on triangular meshes and also studied the effect of finite element spaces on the superconvergence properties of DG solutions on three types of triangular elements and it showed that the DG solution is <i>O(h<sup>p+2</sup>)</i> superconvergent at Legendre points on the outflow edge on triangles having one outflow edge using three polynomial spaces. A posteriori error estimates are tested on a number of linear and nonlinear problems to show their efficiency and accuracy under lattice refinement for smooth and discontinuous solutions.\u0000","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141388673","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}
Pub Date : 2024-05-10DOI: 10.11648/j.acm.20241303.11
Basma Mohamed, Mohammed Badawy
One area of graph theory that has been studied in great detail is dominance in graphs. Applications for dominating sets are numerous. In wireless networking, dominant sets are used to find effective paths inside ad hoc mobile networks. They have also been used in the creation of document summaries and safe electrical grid systems. A set S⊆V is said to be dominating set of G if for every v є V-S there exists a vertex u є S such that uv є E. The dominance number of G, represented by γ(G), is the lowest cardinality of vertices among the dominating set of G. A classic NP-complete decision problem in computational complexity theory determines whether, given a graph G and input K, γ(G) ≤ K. This is known as the dominating set issue. Consequently, it is thought that calculating γ(G) for each given graph G may not be possible to do with a feasible algorithm. In addition to efficient approximation tactics, there exist efficient exact techniques for various graph classes. If there are no neighboring vertices in a subset S, then S⊆V is an independent set. Additionally, the empty set and the subset with just one vertex are independent. An independent dominating set of G is a set S of vertices in a graph G that is both an independent and a dominating set of G. This paper's primary goal is to investigate the dominance and independent dominating set of many graphs, including the line graph, the alternate triangular belt graph, the bistar graph, the triangular snake graph, and others.
图论的一个研究领域是图中的支配性。支配集的应用非常广泛。在无线网络中，支配集被用于在特设移动网络中寻找有效路径。它们还被用于创建文件摘要和安全电网系统。如果对每一个 vє V-S 都存在一个顶点 uє S，使得 uv є E，那么集合 S⊆V 就被称为 G 的支配集。因此，对于每个给定的图 G，计算 γ(G)可能无法用可行的算法来完成。除了高效的近似策略外，还有针对各种图类的高效精确技术。如果子集 S 中没有相邻顶点，那么 S⊆V 就是一个独立集。此外，空集和只有一个顶点的子集也是独立的。本文的主要目标是研究线图、交替三角带图、双星图、三角蛇图等多种图的支配性和独立支配集。
{"title":"Some New Results on Domination and Independent Dominating Set of Some Graphs","authors":"Basma Mohamed, Mohammed Badawy","doi":"10.11648/j.acm.20241303.11","DOIUrl":"https://doi.org/10.11648/j.acm.20241303.11","url":null,"abstract":"One area of graph theory that has been studied in great detail is dominance in graphs. Applications for dominating sets are numerous. In wireless networking, dominant sets are used to find effective paths inside ad hoc mobile networks. They have also been used in the creation of document summaries and safe electrical grid systems. A set <I>S</I>⊆<I>V</I> is said to be dominating set of <I>G</I> if for every <i>v </i>є <I>V</I>-<I>S</I> there exists a vertex <i>u</i> є <I>S</I> such that <i>uv</i> є <I>E</I>. The dominance number of <I>G</I>, represented by <i>γ</i>(<I>G</I>), is the lowest cardinality of vertices among the dominating set of <I>G</I>. A classic NP-complete decision problem in computational complexity theory determines whether, given a graph <I>G</I> and input <I>K</I>, <i>γ</i>(<I>G</I>) ≤ <I>K</I>. This is known as the dominating set issue. Consequently, it is thought that calculating <i>γ</i>(<I>G</I>) for each given graph <I>G</I> may not be possible to do with a feasible algorithm. In addition to efficient approximation tactics, there exist efficient exact techniques for various graph classes. If there are no neighboring vertices in a subset <I>S</I>, then <I>S</I>⊆<I>V</I> is an independent set. Additionally, the empty set and the subset with just one vertex are independent. An independent dominating set of <I>G</I> is a set <I>S</I> of vertices in a graph <I>G</I> that is both an independent and a dominating set of <I>G</I>. This paper's primary goal is to investigate the dominance and independent dominating set of many graphs, including the line graph, the alternate triangular belt graph, the bistar graph, the triangular snake graph, and others.\u0000","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140992896","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}
Pub Date : 2024-02-28DOI: 10.11648/j.acm.20241301.12
Victor Kaigalula, Samuel Mutua
This paper examine numerical study for soret and dufour effects on unsteady Newtonian MHD fluid flow with mass and heat transfer in a collapsible elastic tube using Spectral Collocation technique. The objective of the study is to determine the velocity, temperature and concentration profiles together with heat and mass transfer rates. The governing equations are continuity, momentum, energy and concentration equation. The system of nonlinear partial differential equations governing the flow solved numerically by applying collocation method and implemented in MATLAB. The numerical solution of the profiles displayed both by graphically and numerically for different values of the physical parameters. The effects of varying various parameters such as Reynolds number, Hartmann number, Soret number, Dufour number and Prandtl number on velocity, temperature and concentration profiles also the rates of heat and mass transfer are discussed. The findings of this study are important due to its wide range of application including but not limited to medical fields, biological sciences and other physical sciences where collapsible tubes are applied.
{"title":"Soret and Dufour Effects on MHD Fluid Flow Through a Collapssible Tube Using Spectral Based Collocation Method","authors":"Victor Kaigalula, Samuel Mutua","doi":"10.11648/j.acm.20241301.12","DOIUrl":"https://doi.org/10.11648/j.acm.20241301.12","url":null,"abstract":"This paper examine numerical study for soret and dufour effects on unsteady Newtonian MHD fluid flow with mass and heat transfer in a collapsible elastic tube using Spectral Collocation technique. The objective of the study is to determine the velocity, temperature and concentration profiles together with heat and mass transfer rates. The governing equations are continuity, momentum, energy and concentration equation. The system of nonlinear partial differential equations governing the flow solved numerically by applying collocation method and implemented in MATLAB. The numerical solution of the profiles displayed both by graphically and numerically for different values of the physical parameters. The effects of varying various parameters such as Reynolds number, Hartmann number, Soret number, Dufour number and Prandtl number on velocity, temperature and concentration profiles also the rates of heat and mass transfer are discussed. The findings of this study are important due to its wide range of application including but not limited to medical fields, biological sciences and other physical sciences where collapsible tubes are applied.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140417158","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}
Pub Date : 2023-11-01DOI: 10.11648/j.acm.20231205.12
Dandan Ye, Fei Zhang, Yiteng Qin, Xiaojuan Zhang, Ning Zhang, Jin Qin, Wei Chen, Yingze Zhang
{"title":"Trapping Issues for Weight-dependent Walks in the Weighted Extended Cayley Networks","authors":"Dandan Ye, Fei Zhang, Yiteng Qin, Xiaojuan Zhang, Ning Zhang, Jin Qin, Wei Chen, Yingze Zhang","doi":"10.11648/j.acm.20231205.12","DOIUrl":"https://doi.org/10.11648/j.acm.20231205.12","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139302447","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}
Pub Date : 2023-10-19DOI: 10.30546/1683-6154.22.4.2023.443
Yan-Fang Li, D. Lim, Feng Qi
In the paper, by virtue of the famous formula of Fa`a di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of other techniques, the authors establish closed-form formulas in terms of the Bernoulli numbers and the second kind Stirling numbers, present determinantal expressions, derive recursive relations, obtain power series, and compute special values of the function $frac{v^j}{1-operatorname{e}^{-v}}$, its derivatives, and related ones used in Clark--Ismail's two conjectures. By these results, the authors also discover a formula for the determinant of a Hessenberg matrix and derive logarithmic convexity of a sequence related to the function and its derivatives.
在这篇论文中，作者通过 Fa`a di Bruno 的著名公式，借助贝尔局部多项式的几个等式，通过两个可微分函数之比导数的公式，并利用其他技术、作者建立了伯努利数和第二类斯特林数的闭式公式，提出了行列式表达式，推导了递推关系，获得了幂级数，并计算了函数 $/frac{v^j}{1-operatorname{e}^{-v}}$、其导数以及克拉克-伊斯梅尔的两个猜想中使用的相关导数的特殊值。通过这些结果，作者还发现了海森堡矩阵的行列式公式，并推导出与函数及其导数相关的序列的对数凸性。
{"title":"Closed-form formulas, determinantal expressions, recursive relations, power series, and special values of several functions used in Clark–İsmail’s two conjectures","authors":"Yan-Fang Li, D. Lim, Feng Qi","doi":"10.30546/1683-6154.22.4.2023.443","DOIUrl":"https://doi.org/10.30546/1683-6154.22.4.2023.443","url":null,"abstract":"In the paper, by virtue of the famous formula of Fa`a di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of other techniques, the authors establish closed-form formulas in terms of the Bernoulli numbers and the second kind Stirling numbers, present determinantal expressions, derive recursive relations, obtain power series, and compute special values of the function $frac{v^j}{1-operatorname{e}^{-v}}$, its derivatives, and related ones used in Clark--Ismail's two conjectures. By these results, the authors also discover a formula for the determinant of a Hessenberg matrix and derive logarithmic convexity of a sequence related to the function and its derivatives.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139316771","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}
Pub Date : 2023-09-25DOI: 10.11648/j.acm.20231205.11
Ildikó Somogyi, Anna Soós
Fractal interpolation methods became an important method in data processing, even for functions with abrupt changes. In the last few decades it has attracted several authors because it can be applied in various fields. The advantage of these methods are that we can generalize the classical approximation methods and also we can combine these methods for example with Lagrange interpolation, Hermite interpolation or spline interpolation. The classical Lagrange interpolation problem give the construction of a suitable approximate function based on the values of the function on given points. These method was generalized for more than one variable functions. In this article we generalize the so-called algebraic maximal Lagrange interpolation formula in order to approximate functions on a rectangular domain with fractal functions. The construction of the fractal function is made with a so-called iterated function system. This method it has the advantage that all classical methods can be obtained as a particular case of a fractal function. We also use the construction for a polynomial type fractal function and we proof that the Lagrange-type algebraic minimal bivariate fractal function satisfies the required interpolation conditions. Also we give a delimitation of the error, using the result regarding the error of a polynomial fractal interpolation function.
{"title":"Lagrange-type Algebraic Minimal Bivariate Fractal Interpolation Formula","authors":"Ildikó Somogyi, Anna Soós","doi":"10.11648/j.acm.20231205.11","DOIUrl":"https://doi.org/10.11648/j.acm.20231205.11","url":null,"abstract":"Fractal interpolation methods became an important method in data processing, even for functions with abrupt changes. In the last few decades it has attracted several authors because it can be applied in various fields. The advantage of these methods are that we can generalize the classical approximation methods and also we can combine these methods for example with Lagrange interpolation, Hermite interpolation or spline interpolation. The classical Lagrange interpolation problem give the construction of a suitable approximate function based on the values of the function on given points. These method was generalized for more than one variable functions. In this article we generalize the so-called algebraic maximal Lagrange interpolation formula in order to approximate functions on a rectangular domain with fractal functions. The construction of the fractal function is made with a so-called iterated function system. This method it has the advantage that all classical methods can be obtained as a particular case of a fractal function. We also use the construction for a polynomial type fractal function and we proof that the Lagrange-type algebraic minimal bivariate fractal function satisfies the required interpolation conditions. Also we give a delimitation of the error, using the result regarding the error of a polynomial fractal interpolation function.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135865299","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}
Pub Date : 2023-07-21DOI: 10.11648/j.acm.20231204.12
Jianbing Cao, Cheng Zhang, S. Arjika
{"title":"A <i>q</i>-Operational Equation for Carlitz’s <i>q</i>-Operators with Some Applications","authors":"Jianbing Cao, Cheng Zhang, S. Arjika","doi":"10.11648/j.acm.20231204.12","DOIUrl":"https://doi.org/10.11648/j.acm.20231204.12","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78112145","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}
Pub Date : 2023-07-21DOI: 10.11648/j.acm.20231204.11
M. Nithya, K. Bhuvaneswari, S. Senthil
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