Göppel, Simon; Frikel, Jürgen; Haltmeier, Markus Translation invariant diagonal frame decomposition of inverse problems and their regularization. (English) Zbl 1515.65143 Inverse Probl. 39, No. 6, Article ID 065011, 21 p. (2023). MSC: 65J22 65J20 PDFBibTeX XMLCite \textit{S. Göppel} et al., Inverse Probl. 39, No. 6, Article ID 065011, 21 p. (2023; Zbl 1515.65143) Full Text: DOI arXiv
Egidi, Nadaniela; Giacomini, Josephin; Maponi, Pierluigi; Youssef, Michael An FFT method for the numerical differentiation. (English) Zbl 1511.65017 Appl. Math. Comput. 445, Article ID 127856, 13 p. (2023). MSC: 65D25 65T50 45P05 65R20 PDFBibTeX XMLCite \textit{N. Egidi} et al., Appl. Math. Comput. 445, Article ID 127856, 13 p. (2023; Zbl 1511.65017) Full Text: DOI
Zhao, Zhenyu A Hermite extension method for numerical differentiation. (English) Zbl 1461.65025 Appl. Numer. Math. 159, 46-60 (2021). MSC: 65D25 26A24 PDFBibTeX XMLCite \textit{Z. Zhao}, Appl. Numer. Math. 159, 46--60 (2021; Zbl 1461.65025) Full Text: DOI
Lagergren, John H.; Nardini, John T.; Lavigne, G. Michael; Rutter, Erica M.; Flores, Kevin B. Learning partial differential equations for biological transport models from noisy spatio-temporal data. (English) Zbl 1439.35493 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190800, 21 p. (2020). MSC: 35Q92 62F10 92B20 PDFBibTeX XMLCite \textit{J. H. Lagergren} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190800, 21 p. (2020; Zbl 1439.35493) Full Text: DOI arXiv Link
Hong, Han; Mahajan, Aprajit; Nekipelov, Denis Extremum estimation and numerical derivatives. (English) Zbl 1337.62057 J. Econom. 188, No. 1, 250-263 (2015). MSC: 62G05 65C60 62F12 62G20 62P20 PDFBibTeX XMLCite \textit{H. Hong} et al., J. Econom. 188, No. 1, 250--263 (2015; Zbl 1337.62057) Full Text: DOI
Li, Ming; Wang, Yujiao; Ling, Leevan Numerical Caputo differentiation by radial basis functions. (English) Zbl 1309.62159 J. Sci. Comput. 62, No. 1, 300-315 (2015). MSC: 62M40 65D25 65F22 PDFBibTeX XMLCite \textit{M. Li} et al., J. Sci. Comput. 62, No. 1, 300--315 (2015; Zbl 1309.62159) Full Text: DOI
McDevitt, Timothy J. Discrete Lanczos derivatives of noisy data. (English) Zbl 1259.65051 Int. J. Comput. Math. 89, No. 7, 916-931 (2012). MSC: 65D25 PDFBibTeX XMLCite \textit{T. J. McDevitt}, Int. J. Comput. Math. 89, No. 7, 916--931 (2012; Zbl 1259.65051) Full Text: DOI
Hu, Bang; Lu, Shuai Numerical differentiation by a Tikhonov regularization method based on the discrete cosine transform. (English) Zbl 1237.65017 Appl. Anal. 91, No. 4, 719-736 (2012). MSC: 65D25 65J20 PDFBibTeX XMLCite \textit{B. Hu} and \textit{S. Lu}, Appl. Anal. 91, No. 4, 719--736 (2012; Zbl 1237.65017) Full Text: DOI
Riachy, Samer; Mboup, Mamadou; Richard, Jean-Pierre Multivariate numerical differentiation. (English) Zbl 1252.65060 J. Comput. Appl. Math. 236, No. 6, 1069-1089 (2011). MSC: 65D25 41A63 41A10 94A12 PDFBibTeX XMLCite \textit{S. Riachy} et al., J. Comput. Appl. Math. 236, No. 6, 1069--1089 (2011; Zbl 1252.65060) Full Text: DOI
Bauer, Frank; Lukas, Mark A. Comparing parameter choice methods for regularization of ill-posed problems. (English) Zbl 1220.65063 Math. Comput. Simul. 81, No. 9, 1795-1841 (2011). MSC: 65J10 65J20 65J22 47A52 PDFBibTeX XMLCite \textit{F. Bauer} and \textit{M. A. Lukas}, Math. Comput. Simul. 81, No. 9, 1795--1841 (2011; Zbl 1220.65063) Full Text: DOI
Zhang, Haizhang; Zhang, Qinghui Sparse discretization matrices for Volterra integral operators with applications to numerical differentiation. (English) Zbl 1246.65255 J. Integral Equations Appl. 23, No. 1, 137-156 (2011). Reviewer: Pierluigi Maponi (Camerino) MSC: 65R20 65D25 45D05 PDFBibTeX XMLCite \textit{H. Zhang} and \textit{Q. Zhang}, J. Integral Equations Appl. 23, No. 1, 137--156 (2011; Zbl 1246.65255) Full Text: DOI
Anderssen, R. S.; Hegland, M. Derivative spectroscopy – an enhanced role for numerical differentiation. (English) Zbl 1205.65130 J. Integral Equations Appl. 22, No. 3, 355-367 (2010). MSC: 65D25 78A10 PDFBibTeX XMLCite \textit{R. S. Anderssen} and \textit{M. Hegland}, J. Integral Equations Appl. 22, No. 3, 355--367 (2010; Zbl 1205.65130) Full Text: DOI
Zou, Yu; Kavousanakis, Michail E.; Kevrekidis, Ioannis G.; Fox, Rodney O. Coarse-grained computation for particle coagulation and sintering processes by linking quadrature method of moments with Monte-Carlo. (English) Zbl 1346.82037 J. Comput. Phys. 229, No. 14, 5299-5314 (2010). MSC: 82C80 65C05 82B80 92E20 PDFBibTeX XMLCite \textit{Y. Zou} et al., J. Comput. Phys. 229, No. 14, 5299--5314 (2010; Zbl 1346.82037) Full Text: DOI
Ahnert, Karsten; Abel, Markus Numerical differentiation of experimental data: local versus global methods. (English) Zbl 1196.65046 Comput. Phys. Commun. 177, No. 10, 764-774 (2007). MSC: 65D25 PDFBibTeX XMLCite \textit{K. Ahnert} and \textit{M. Abel}, Comput. Phys. Commun. 177, No. 10, 764--774 (2007; Zbl 1196.65046) Full Text: DOI arXiv
Lukas, Mark A.; Shi, Mingren Sensitivity analysis of constrained linear \(L_1\) regression: Perturbations to constraints, addition and deletion of observations. (English) Zbl 1157.62462 Comput. Stat. Data Anal. 51, No. 2, 1213-1231 (2006). MSC: 62J05 62F30 62J20 62F10 65C60 62G08 PDFBibTeX XMLCite \textit{M. A. Lukas} and \textit{M. Shi}, Comput. Stat. Data Anal. 51, No. 2, 1213--1231 (2006; Zbl 1157.62462) Full Text: DOI
Ahn, Soyoung; Choi, U. Jin; Ramm, Alexander G. A scheme for stable numerical differentiation. (English) Zbl 1086.65013 J. Comput. Appl. Math. 186, No. 2, 325-334 (2006). Reviewer: John Pryce (Swindon) MSC: 65D25 PDFBibTeX XMLCite \textit{S. Ahn} et al., J. Comput. Appl. Math. 186, No. 2, 325--334 (2006; Zbl 1086.65013) Full Text: DOI
Shi, Mingren; Lukas, Mark A. Sensitivity analysis of constrained linear \(L_1\) regression: perturbations to response and predictor variables. (English) Zbl 1429.62300 Comput. Stat. Data Anal. 48, No. 4, 779-802 (2005). MSC: 62J05 PDFBibTeX XMLCite \textit{M. Shi} and \textit{M. A. Lukas}, Comput. Stat. Data Anal. 48, No. 4, 779--802 (2005; Zbl 1429.62300) Full Text: DOI
Li, Jianping General explicit difference formulas for numerical differentiation. (English) Zbl 1077.65021 J. Comput. Appl. Math. 183, No. 1, 29-52 (2005). Reviewer: Iulian Coroian (Baia Mare) MSC: 65D25 15A06 65L12 15A15 PDFBibTeX XMLCite \textit{J. Li}, J. Comput. Appl. Math. 183, No. 1, 29--52 (2005; Zbl 1077.65021) Full Text: DOI
Ramm, Alexander G.; Smirnova, Alexandra B. On stable numerical differentiation. (English) Zbl 0973.65015 Math. Comput. 70, No. 235, 1131-1153 (2001). Reviewer: Luigi Gatteschi (Torino) MSC: 65D25 65R30 65J20 PDFBibTeX XMLCite \textit{A. G. Ramm} and \textit{A. B. Smirnova}, Math. Comput. 70, No. 235, 1131--1153 (2001; Zbl 0973.65015) Full Text: DOI
Spivack, M.; Reeve, D. E. Recovery of a variable coefficient in a coastal evolution equation. (English) Zbl 1023.86001 J. Comput. Phys. 151, No. 2, 585-596 (1999). MSC: 86A05 86-08 PDFBibTeX XMLCite \textit{M. Spivack} and \textit{D. E. Reeve}, J. Comput. Phys. 151, No. 2, 585--596 (1999; Zbl 1023.86001) Full Text: DOI Link
Anderssen, Bob; de Hoog, Frank; Hegland, Markus A stable finite difference ansatz for higher order differentiation of non-exact data. (English) Zbl 0918.65017 Bull. Aust. Math. Soc. 58, No. 2, 223-232 (1998). Reviewer: J.L.Fernández Muñiz (Puebla) MSC: 65D25 PDFBibTeX XMLCite \textit{B. Anderssen} et al., Bull. Aust. Math. Soc. 58, No. 2, 223--232 (1998; Zbl 0918.65017) Full Text: DOI
Lukas, Mark A. On the discrepancy principle and generalised maximum likelihood for regularisation. (English) Zbl 0840.65043 Bull. Aust. Math. Soc. 52, No. 3, 399-424 (1995). Reviewer: Yu Wenhuan (Tianjin) MSC: 65J10 65J20 65R30 62G05 PDFBibTeX XMLCite \textit{M. A. Lukas}, Bull. Aust. Math. Soc. 52, No. 3, 399--424 (1995; Zbl 0840.65043) Full Text: DOI
Anderssen, R. S.; Latham, G. A.; Westcott, M. Statistical methodology for inverse problems. (English) Zbl 0843.62093 Math. Comput. Modelling 22, No. 10-12, 1-5 (1995). MSC: 62M20 65C99 65R20 PDFBibTeX XMLCite \textit{R. S. Anderssen} et al., Math. Comput. Modelling 22, No. 10--12, 1--5 (1995; Zbl 0843.62093) Full Text: DOI
Hegland, Markus Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization. (English) Zbl 0841.65039 Appl. Anal. 59, No. 1-4, 207-223 (1995). Reviewer: M.Hegland (Canberra) MSC: 65J10 65R20 65R30 47A50 65J20 45B05 46E35 PDFBibTeX XMLCite \textit{M. Hegland}, Appl. Anal. 59, No. 1--4, 207--223 (1995; Zbl 0841.65039) Full Text: DOI
Fioretti, S.; Jetto, L. Accurate derivative estimation from noisy data: A state-space approach. (English) Zbl 0663.93065 Int. J. Syst. Sci. 20, No. 1, 33-53 (1989). MSC: 93E10 60G35 93E14 93E11 93E25 65D25 PDFBibTeX XMLCite \textit{S. Fioretti} and \textit{L. Jetto}, Int. J. Syst. Sci. 20, No. 1, 33--53 (1989; Zbl 0663.93065) Full Text: DOI
Liskovets, O. A. Theory and the methods of solution of ill-posed problems. (English) Zbl 0595.65056 J. Sov. Math. 34, 1656-1696 (1986). MSC: 65J05 65R20 65-02 47A50 PDFBibTeX XMLCite \textit{O. A. Liskovets}, J. Sov. Math. 34, 1656--1696 (1986; Zbl 0595.65056) Full Text: DOI
Miel, George; Mooney, Rose On the condition number of Lagrangian numerical differentiation. (English) Zbl 0602.65007 Appl. Math. Comput. 16, 241-252 (1985). Reviewer: A.de Castro MSC: 65D25 PDFBibTeX XMLCite \textit{G. Miel} and \textit{R. Mooney}, Appl. Math. Comput. 16, 241--252 (1985; Zbl 0602.65007) Full Text: DOI
Brunner, Hermann A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations. (English) Zbl 0485.65087 J. Comput. Appl. Math. 8, 213-229 (1982). MSC: 65R20 65-02 45E10 45J05 45D05 PDFBibTeX XMLCite \textit{H. Brunner}, J. Comput. Appl. Math. 8, 213--229 (1982; Zbl 0485.65087) Full Text: DOI
Oliver, J. An algorithm for numerical differentiation of a function of one real variable. (English) Zbl 0439.65013 J. Comput. Appl. Math. 6, 145-160 (1980). MSC: 65D25 65-04 PDFBibTeX XMLCite \textit{J. Oliver}, J. Comput. Appl. Math. 6, 145--160 (1980; Zbl 0439.65013) Full Text: DOI
Cullum, Jane The effective choice of the smoothing norm in regularization. (English) Zbl 0406.65055 Math. Comput. 33, 149-170 (1979). MSC: 65R20 45A05 45L05 65F35 PDFBibTeX XMLCite \textit{J. Cullum}, Math. Comput. 33, 149--170 (1979; Zbl 0406.65055) Full Text: DOI
Micchelli, C. A. On an optimal method for the numerical differentiation of smooth functions. (English) Zbl 0357.65013 J. Approximation Theory 18, 189-204 (1976). MSC: 65D25 PDFBibTeX XMLCite \textit{C. A. Micchelli}, J. Approx. Theory 18, 189--204 (1976; Zbl 0357.65013) Full Text: DOI
Ekstrom, M. P.; Rhoads, R. L. On the application of eigenvector expansions to numerical deconvolution. (English) Zbl 0279.65107 J. Comput. Phys. 14, 319-340 (1974). MSC: 65R20 PDFBibTeX XMLCite \textit{M. P. Ekstrom} and \textit{R. L. Rhoads}, J. Comput. Phys. 14, 319--340 (1974; Zbl 0279.65107) Full Text: DOI