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On the rate of convergence of modified (alpha)-Bernstein operators based on q-integers 基于q-整数的改进(alpha) -Bernstein算子的收敛速度
Journal of Numerical Analysis and Approximation Theory Pub Date : 2022-09-17 DOI: 10.33993/jnaat511-1244
P. Agrawal, Dharmendra Kumar, Behar Baxhaku
{"title":"On the rate of convergence of modified (alpha)-Bernstein operators based on q-integers","authors":"P. Agrawal, Dharmendra Kumar, Behar Baxhaku","doi":"10.33993/jnaat511-1244","DOIUrl":"https://doi.org/10.33993/jnaat511-1244","url":null,"abstract":"In the present paper we define a q-analogue of the modified a-Bernstein operators introduced by Kajla and Acar (Ann. Funct. Anal. 10 (4) 2019, 570-582). We study uniform convergence theorem and the Voronovskaja type asymptotic theorem. We determine the estimate of error in the approximation by these operators by virtue of second order modulus of continuity via the approach of Steklov means and the technique of Peetre's (K)-functional. Next, we investigate the Gruss- Voronovskaya type theorem. Further, we define a bivariate tensor product of these operatos and derive the convergence estimates by utilizing the partial and total moduli of continuity. The approximation degree by means of Peetre's K- functional , the Voronovskaja and Gruss Voronovskaja type theorems are also investigated. Lastly, we construct the associated GBS (Generalized Boolean Sum) operator and examine its convergence behavior by virtue of the mixed modulus of smoothness.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114262060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Basins of attraction for family of Popovski’s methods and their extension to multiple roots 波波夫斯基方法家族的吸引力盆地及其对多重根的推广
Journal of Numerical Analysis and Approximation Theory Pub Date : 2022-09-17 DOI: 10.33993/jnaat511-1248
B. Neta
{"title":"Basins of attraction for family of Popovski’s methods and their extension to multiple roots","authors":"B. Neta","doi":"10.33993/jnaat511-1248","DOIUrl":"https://doi.org/10.33993/jnaat511-1248","url":null,"abstract":"In this paper we revisit Popovski’s family of methods for simple roots. We compare several members using basins of attraction visually and qualitatively by comparing the run-time on several examples, the average number of iterations and the number of divergent points. We chose 5 different members of the family. We also develop an equivalent family of methods for multiple roots and compare several members on six different numerical examples.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133251091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A note on the unique solvability condition for generalized absolute value matrix equation 关于广义绝对值矩阵方程唯一可解条件的注记
Journal of Numerical Analysis and Approximation Theory Pub Date : 2022-09-17 DOI: 10.33993/jnaat511-1263
Shubham Kumar, .. Deepmala
{"title":"A note on the unique solvability condition for generalized absolute value matrix equation","authors":"Shubham Kumar, .. Deepmala","doi":"10.33993/jnaat511-1263","DOIUrl":"https://doi.org/10.33993/jnaat511-1263","url":null,"abstract":"The spectral radius condition [rho (vert A^{-1} vertcdot vert B vert)<1]for the unique solvability of generalized absolute value matrix equation (GAVME) [AX + B vert X vert = D] is provided. For some instances, our condition is superior to the earlier published singular values conditions (sigma_{max}(vert B vert)<sigma_{min}(A)) [M. Dehghan, 2020] and (sigma_{max}(B)<sigma_{min}(A)) [Kai Xie, 2021]. For the validity of our condition, we also provided an example.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121713478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Integer composition, connection Appell constants and Bell polynomials 整数组成，连接阿佩尔常数和贝尔多项式
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-12-31 DOI: 10.33993/jnaat502-1245
N. Luno
{"title":"Integer composition, connection Appell constants and Bell polynomials","authors":"N. Luno","doi":"10.33993/jnaat502-1245","DOIUrl":"https://doi.org/10.33993/jnaat502-1245","url":null,"abstract":"We introduce an explicit form of the connection coefficients for Appell polynomial sequences via Toeplitz-Hessenberg matrix determinants.\u0000Generalizing, we give an explicit form of the connection coefficients for arbitrary   polynomial sequences and constitute the combinatorial meaning of both constants in terms of integer composition.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124897236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extending the solvability of equations using secant-type methods in Banach space 用割型方法在Banach空间中扩展方程的可解性
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-12-31 DOI: 10.33993/jnaat502-1134
I. Argyros, S. George
{"title":"Extending the solvability of equations using secant-type methods in Banach space","authors":"I. Argyros, S. George","doi":"10.33993/jnaat502-1134","DOIUrl":"https://doi.org/10.33993/jnaat502-1134","url":null,"abstract":"We extend the solvability of equations dened on a Banach space using numerically ecient secant-type methods. The convergence domain of these methods is enlarged using our new idea of restricted convergence region. By using this approach, we obtain a more precise location where the iterates lie than in earlier studies leading to tighter Lipschitz constants. This way the semi-local convergence produces weaker sucient convergence criteria and tighter error bounds than in earlier works. These improvements are also obtained under the same computational eort, since the new Lipschitz constants are special cases of the old ones.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132219719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the development and extensions of some classes of optimal three-point iterations for solving nonlinear equations 求解非线性方程的几类最优三点迭代的发展与推广
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-12-31 DOI: 10.33993/jnaat502-1238
T. Zhanlav, Otgondorj Khuder
{"title":"On the development and extensions of some classes of optimal three-point iterations for solving nonlinear equations","authors":"T. Zhanlav, Otgondorj Khuder","doi":"10.33993/jnaat502-1238","DOIUrl":"https://doi.org/10.33993/jnaat502-1238","url":null,"abstract":"We develop a new families of optimal eight--order methods for solving nonlinear equations. We also extend some classes of optimal methods for any suitable choice of iteration parameter. Such development and extension was made using sufficient convergence conditions given in [14]. Numerical examples are considered to check the convergence order of new families and extensions of some well-known methods.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125219741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A catalogue of mathematical formulas involving (pi), with analysis 包含(pi)和分析的数学公式目录
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-12-31 DOI: 10.33993/jnaat502-1259
D. Bailey
{"title":"A catalogue of mathematical formulas involving (pi), with analysis","authors":"D. Bailey","doi":"10.33993/jnaat502-1259","DOIUrl":"https://doi.org/10.33993/jnaat502-1259","url":null,"abstract":"This paper presents a catalogue of mathematical formulas and iterative algorithms for evaluating the mathematical constant (pi), ranging from Archimedes' 2200-year-old iteration to some formulas that were discovered only in the past few decades. Computer implementations and timing results for these formulas and algorithms are also included. In particular, timings are presented for evaluations of various infinite series formulas to approximately 10,000-digit precision, for evaluations of various integral formulas to approximately 4,000-digit precision, and for evaluations of several iterative algorithms to approximately 100,000-digit precision, all based on carefully designed comparative computer runs.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117035717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Asymptotic formula in simultaneous approximation for certain Ismail-May-Baskakov operators 一类Ismail-May-Baskakov算子的同时逼近渐近公式
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-12-31 DOI: 10.33993/jnaat502-1235
Vijay Gupta, M. Rassias
{"title":"Asymptotic formula in simultaneous approximation for certain Ismail-May-Baskakov operators","authors":"Vijay Gupta, M. Rassias","doi":"10.33993/jnaat502-1235","DOIUrl":"https://doi.org/10.33993/jnaat502-1235","url":null,"abstract":"In the present paper, we introduce a modification of Ismail-May operators having weights of Baskakov basis functions. We estimate weighted Korovkin's theorem and difference estimates between two operators and establish a Voronovskaja type asymptotic formula in simultaneous approximation.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127147363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some inequalities for a Stancu type operator via (1,1) box convex functions 通过(1,1)盒凸函数的Stancu型算子的一些不等式
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-11-19 DOI: 10.33993/jnaat501-1242
I. Gavrea, Daniel Ianoşi
{"title":"Some inequalities for a Stancu type operator via (1,1) box convex functions","authors":"I. Gavrea, Daniel Ianoşi","doi":"10.33993/jnaat501-1242","DOIUrl":"https://doi.org/10.33993/jnaat501-1242","url":null,"abstract":"In this paper we introduce a Stancu type operator and we prove inequalities of Rașa's type.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124262333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation by matrix transform in generalized grand Lebesgue spaces with variable exponent 变指数广义大Lebesgue空间中的矩阵变换逼近
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-11-19 DOI: 10.33993/jnaat501-1234
A. Testici, D. Israfilov
{"title":"Approximation by matrix transform in generalized grand Lebesgue spaces with variable exponent","authors":"A. Testici, D. Israfilov","doi":"10.33993/jnaat501-1234","DOIUrl":"https://doi.org/10.33993/jnaat501-1234","url":null,"abstract":"In this work the Lipschitz subclass of the generalized grand Lebesgue space with variable exponent is defined and the error of approximation by matrix transforms in this subclass is estimated.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127023783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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