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## Renka, Robert J.

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 Author ID: renka.robert-j Published as: Renka, R. J.; Renka, Robert; Renka, Robert J.
 Documents Indexed: 49 Publications since 1984
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#### Co-Authors

 26 single-authored 10 Neuberger, John W. 3 Brown, Ron 3 Kazemi, Parimah 2 Cline, Alan K. 1 Griffith, Cheryl A. 1 Knowles, Ian Walker 1 Lapidus, Michel L. 1 Leung, N. K. 1 Linnér, Anders 1 Roberts, Stephen Gwyn 1 Testa, Frank J. 1 Zoppou, Christopher
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#### Serials

 20 ACM Transactions on Mathematical Software 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 SIAM Journal on Scientific Computing 4 Electronic Journal of Differential Equations (EJDE) 3 Experimental Mathematics 2 Computer Aided Geometric Design 2 Applied Numerical Mathematics 1 International Journal for Numerical Methods in Fluids 1 Rocky Mountain Journal of Mathematics 1 Applied Mathematics and Computation 1 International Journal for Numerical Methods in Engineering 1 SIAM Journal on Numerical Analysis 1 SIAM Journal on Scientific and Statistical Computing 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear and Convex Analysis 1 Central European Journal of Mathematics
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#### Fields

 46 Numerical analysis (65-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Partial differential equations (35-XX) 6 Approximations and expansions (41-XX) 4 Differential geometry (53-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Fluid mechanics (76-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Operations research, mathematical programming (90-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of deformable solids (74-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

39 Publications have been cited 336 times in 255 Documents Cited by Year
Multivariate interpolation of large sets of scattered data. Zbl 0642.65006
Renka, Robert J.
1988
A triangle-based $$C^ 1$$ interpolation method. Zbl 0568.65006
Renka, R. J.; Cline, A. K.
1984
Algorithm 792: Accuracy tests of ACM algorithms for interpolation of scattered data in the plane. Zbl 0963.65014
Renka, Robert J.; Brown, Ron
1999
Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere. Zbl 0903.65111
Renka, Robert J.
1997
Snowflake harmonics and computer graphics: Numerical computation of spectra on fractal drums. Zbl 0920.73165
Lapidus, Michel L.; Neuberger, J. W.; Renka, Robert J.; Griffith, Cheryl A.
1996
Algorithm 660 QSHEP2D: Quadratic Shepard method for bivariate interpolation of scattered data. Zbl 0709.65504
Renka, Robert J.
1988
Interpolation of data on the surface of a sphere. Zbl 0548.65001
Renka, Robert J.
1984
Minimal surfaces and Sobolev gradients. Zbl 0857.35004
Renka, R. J.; Neuberger, J. W.
1995
A constrained two-dimensional triangulation and the solution of closest node problems in the presence of barriers. Zbl 0714.65024
Cline, A. K.; Renka, R. J.
1990
Constructing fair curves and surfaces with a Sobolev gradient method. Zbl 1069.65565
Renka, Robert J.
2004
Sobolev gradients and the Ginzburg-Landau functional. Zbl 0920.35059
Neuberger, J. W.; Renka, R. J.
1999
Interpolatory tension splines with automatic selection of tension factors. Zbl 0629.65009
Renka, R. J.
1987
Methods for numerical differentiation of noisy data. Zbl 1287.65016
Knowles, Ian; Renka, Robert J.
2014
Image segmentation with a Sobolev gradient method. Zbl 1238.94009
Renka, R. J.
2009
Nonlinear least squares and Sobolev gradients. Zbl 1260.65060
Renka, Robert J.
2013
A Levenberg-Marquardt method based on Sobolev gradients. Zbl 1248.49040
Kazemi, Parimah; Renka, Robert J.
2012
Sobolev gradients: introduction, applications, problems. Zbl 1064.35006
Neuberger, J. W.; Renka, R. J.
2004
Algorithm 751: TRIPACK: A constrained two-dimensional Delaunay triangulation package. Zbl 0884.65144
Renka, R. J.
1996
Algorithm 716: TSPACK: Tension spline curve-fitting package. Zbl 0889.65007
Renka, R. J.
1993
Algorithm 661 QSHEP3D: Quadratic Shepard method for trivariate interpolation of scattered data. Zbl 0709.65502
Renka, Robert J.
1988
Algorithm 790: CSHEP2D: Cubic Shepard method for bivariate interpolation of scattered data. Zbl 0963.65012
Renka, Robert J.
1999
Algorithm 773: SSRFPACK: Interpolation of scattered data on the surface of a sphere with a surface under tension. Zbl 0903.65006
Renka, Robert J.
1997
A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations. Zbl 1260.76016
Renka, Robert J.
2013
Algorithm 833: CSRFPACK – interpolation of scattered data with a $$C^1$$ convexity-preserving surface. Zbl 1070.65505
Renka, Robert J.
2004
Exponential spline interpolation in characteristic based scheme for solving the advective-diffusion equation. Zbl 0990.76061
Zoppou, C.; Roberts, S.; Renka, R. J.
2000
Shape-preserving interpolation by fair discrete $$G^3$$ space curves. Zbl 1120.65311
Renka, Robert J.
2005
Computational simulation of vortex phenomena in superconductors. Zbl 1109.82339
Neuberger, John W.; Renka, Robert J.
2003
$$C^{1}$$ convexity-preserving interpolation of scattered data. Zbl 0942.65016
Leung, N. K.; Renka, R. J.
1999
Mesh improvement by minimizing a weighted sum of squared element volumes. Zbl 1352.65540
Renka, Robert J.
2015
A trust region method for constructing triangle-mesh approximations of parametric minimal surfaces. Zbl 1288.65023
Renka, Robert J.
2014
Minimization of the Ginzburg-Landau energy functional by a Sobolev gradient trust-region method. Zbl 1273.65082
Kazemi, P.; Renka, R. J.
2013
A Sobolev gradient method for construction of elastic curves in regular surfaces. Zbl 1224.65041
Renka, R. J.
2005
Least squares and chaotic behavior in initial value problems. Zbl 1071.65175
Neuberger, J. W.; Renka, R. J.
2005
Numerical approximation of critical points of the Ginzburg-Landau functional. Zbl 1042.65553
Neuberger, J. W.; Renka, R. J.
2001
Algorithm 834: glsurf – an interactive surface plotting program using OpenGL. Zbl 1070.65509
Renka, Robert J.
2004
Algorithm 828: DNSPLIN1: discrete nonlinear spline interpolation. Zbl 1070.65507
Renka, Robert J.
2003
Critical points of the Ginzburg-Landau functional on multiply-connected domains. Zbl 0974.65064
Neuberger, J. W.; Renka, R. J.
2000
Algorithm 791: TSHEP2D: Cosine series Shephard method for bivariate interpolation of scattered data. Zbl 0963.65013
Renka, Robert J.; Brown, Ron
1999
Numerical calculation of singularities for Ginzburg-Landau functionals. Zbl 0886.35139
Neuberger, J. W.; Renka, R. J.
1997
Mesh improvement by minimizing a weighted sum of squared element volumes. Zbl 1352.65540
Renka, Robert J.
2015
Methods for numerical differentiation of noisy data. Zbl 1287.65016
Knowles, Ian; Renka, Robert J.
2014
A trust region method for constructing triangle-mesh approximations of parametric minimal surfaces. Zbl 1288.65023
Renka, Robert J.
2014
Nonlinear least squares and Sobolev gradients. Zbl 1260.65060
Renka, Robert J.
2013
A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations. Zbl 1260.76016
Renka, Robert J.
2013
Minimization of the Ginzburg-Landau energy functional by a Sobolev gradient trust-region method. Zbl 1273.65082
Kazemi, P.; Renka, R. J.
2013
A Levenberg-Marquardt method based on Sobolev gradients. Zbl 1248.49040
Kazemi, Parimah; Renka, Robert J.
2012
Image segmentation with a Sobolev gradient method. Zbl 1238.94009
Renka, R. J.
2009
Shape-preserving interpolation by fair discrete $$G^3$$ space curves. Zbl 1120.65311
Renka, Robert J.
2005
A Sobolev gradient method for construction of elastic curves in regular surfaces. Zbl 1224.65041
Renka, R. J.
2005
Least squares and chaotic behavior in initial value problems. Zbl 1071.65175
Neuberger, J. W.; Renka, R. J.
2005
Constructing fair curves and surfaces with a Sobolev gradient method. Zbl 1069.65565
Renka, Robert J.
2004
Sobolev gradients: introduction, applications, problems. Zbl 1064.35006
Neuberger, J. W.; Renka, R. J.
2004
Algorithm 833: CSRFPACK – interpolation of scattered data with a $$C^1$$ convexity-preserving surface. Zbl 1070.65505
Renka, Robert J.
2004
Algorithm 834: glsurf – an interactive surface plotting program using OpenGL. Zbl 1070.65509
Renka, Robert J.
2004
Computational simulation of vortex phenomena in superconductors. Zbl 1109.82339
Neuberger, John W.; Renka, Robert J.
2003
Algorithm 828: DNSPLIN1: discrete nonlinear spline interpolation. Zbl 1070.65507
Renka, Robert J.
2003
Numerical approximation of critical points of the Ginzburg-Landau functional. Zbl 1042.65553
Neuberger, J. W.; Renka, R. J.
2001
Exponential spline interpolation in characteristic based scheme for solving the advective-diffusion equation. Zbl 0990.76061
Zoppou, C.; Roberts, S.; Renka, R. J.
2000
Critical points of the Ginzburg-Landau functional on multiply-connected domains. Zbl 0974.65064
Neuberger, J. W.; Renka, R. J.
2000
Algorithm 792: Accuracy tests of ACM algorithms for interpolation of scattered data in the plane. Zbl 0963.65014
Renka, Robert J.; Brown, Ron
1999
Sobolev gradients and the Ginzburg-Landau functional. Zbl 0920.35059
Neuberger, J. W.; Renka, R. J.
1999
Algorithm 790: CSHEP2D: Cubic Shepard method for bivariate interpolation of scattered data. Zbl 0963.65012
Renka, Robert J.
1999
$$C^{1}$$ convexity-preserving interpolation of scattered data. Zbl 0942.65016
Leung, N. K.; Renka, R. J.
1999
Algorithm 791: TSHEP2D: Cosine series Shephard method for bivariate interpolation of scattered data. Zbl 0963.65013
Renka, Robert J.; Brown, Ron
1999
Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere. Zbl 0903.65111
Renka, Robert J.
1997
Algorithm 773: SSRFPACK: Interpolation of scattered data on the surface of a sphere with a surface under tension. Zbl 0903.65006
Renka, Robert J.
1997
Numerical calculation of singularities for Ginzburg-Landau functionals. Zbl 0886.35139
Neuberger, J. W.; Renka, R. J.
1997
Snowflake harmonics and computer graphics: Numerical computation of spectra on fractal drums. Zbl 0920.73165
Lapidus, Michel L.; Neuberger, J. W.; Renka, Robert J.; Griffith, Cheryl A.
1996
Algorithm 751: TRIPACK: A constrained two-dimensional Delaunay triangulation package. Zbl 0884.65144
Renka, R. J.
1996
Minimal surfaces and Sobolev gradients. Zbl 0857.35004
Renka, R. J.; Neuberger, J. W.
1995
Algorithm 716: TSPACK: Tension spline curve-fitting package. Zbl 0889.65007
Renka, R. J.
1993
A constrained two-dimensional triangulation and the solution of closest node problems in the presence of barriers. Zbl 0714.65024
Cline, A. K.; Renka, R. J.
1990
Multivariate interpolation of large sets of scattered data. Zbl 0642.65006
Renka, Robert J.
1988
Algorithm 660 QSHEP2D: Quadratic Shepard method for bivariate interpolation of scattered data. Zbl 0709.65504
Renka, Robert J.
1988
Algorithm 661 QSHEP3D: Quadratic Shepard method for trivariate interpolation of scattered data. Zbl 0709.65502
Renka, Robert J.
1988
Interpolatory tension splines with automatic selection of tension factors. Zbl 0629.65009
Renka, R. J.
1987
A triangle-based $$C^ 1$$ interpolation method. Zbl 0568.65006
Renka, R. J.; Cline, A. K.
1984
Interpolation of data on the surface of a sphere. Zbl 0548.65001
Renka, Robert J.
1984
all top 5

#### Cited by 428 Authors

 12 Renka, Robert J. 11 Cavoretto, Roberto 10 Dell’Accio, Francesco 9 Cătinaş, Teodora 9 De Rossi, Alessandra 9 Di Tommaso, Filomena 5 Neuberger, John W. 5 Sial, Sultan 4 Allasia, Giampietro 4 Coman, Gheorghe 4 De Marchi, Stefano 4 Foley, Thomas A. 4 Lapidus, Michel L. 4 Raza, Nauman 4 Rossini, Milvia 4 Schumaker, Larry L. 3 Bozzini, Mira 3 Caliari, Marco 3 Cao, Feilong 3 Costabile, Francesco Aldo 3 Du, Qiang 3 Dutkay, Dorin Ervin 3 Francomano, Elisa 3 Jørgensen, Palle E. T. 3 Kazemi, Parimah 3 Lazzaro, Damiana 3 Leiderman, Karin M. 3 Li, Ming 3 Nouisser, Otheman 3 Paliaga, Marta 3 Pottmann, Helmut 3 Richardson, Walter B. jun. 3 Sloan, Ian Hugh 3 Vianello, Marco 2 Banjai, Lehel 2 Beckmann, Jan P. 2 Blaga, Petru P. 2 Brauchart, Johann S. 2 Butt, Asma Rashid 2 Caira, Rosanna 2 Carey, Graham Francis 2 Carlson, Ralph E. 2 Cortez, Ricardo 2 Dagnino, Catterina 2 Erb, Wolfgang 2 Favennec, Yann 2 Feng, Renzhong 2 Field, David A. 2 Fornberg, Bengt 2 Gao, David Yang 2 Goodman, Timothy N. T. 2 He, Chuanjiang 2 Hussain, Malik Zawwar 2 Hussain, Maria 2 Ju, Lili 2 Karátson, János 2 Lamberti, Paola 2 Lasser, Daniel J. 2 Lederman, Carl 2 Mahavier, William Ted 2 Majid, Abdul 2 Mhaskar, Hrushikesh N. 2 Montefusco, Laura Bacchelli 2 Nielson, Gregory M. 2 Patera, Anthony T. 2 Prestin, Jurgen 2 Qiu, Shufang 2 Rogina, Mladen 2 Rousse, Daniel R. 2 Simpson, R. Bruce 2 Speleers, Hendrik 2 Stüttgen, T. 2 Teplyaev, Alexander 2 Wang, Zewen 2 Womersley, Robert S. 2 Wu, Kailiang 2 Xiu, Dongbin 2 Yeşilyurt, Serhat 2 Yuan, Ye 2 Zerroudi, Benaissa 2 Zhou, Yang 2 Zuppa, Carlos 1 Achdou, Yves 1 Ahlborg, Mandy 1 Albin, J. M. P. 1 Alfeld, Peter 1 Alimi, Adel M. 1 Amirfakhrian, Majid 1 Andersen, Leif B. G. 1 Aqeel, Beenish 1 Araya, Rodolfo A. 1 Armentano, María Gabriela 1 Ayers, Paul W. 1 Badawy, Hope T. 1 Bajorin, N. 1 Balasubramani, N. 1 Balima, O. 1 Barnhill, Robert E. 1 Barros, Saulo R. M. 1 Bartel, Felix ...and 328 more Authors
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#### Cited in 88 Serials

 27 Journal of Computational and Applied Mathematics 20 Computer Aided Geometric Design 18 Computers & Mathematics with Applications 18 Applied Mathematics and Computation 17 Journal of Computational Physics 7 Computer Methods in Applied Mechanics and Engineering 7 Numerical Algorithms 6 Applied Numerical Mathematics 4 Mathematics of Computation 4 International Journal for Numerical Methods in Engineering 4 Experimental Mathematics 4 SIAM Journal on Scientific Computing 4 Computational and Applied Mathematics 4 Advances in Computational Mathematics 3 Mathematical Methods in the Applied Sciences 3 BIT 3 Calcolo 3 Mathematics and Computers in Simulation 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Journal of Scientific Computing 3 Computational Statistics and Data Analysis 3 Mathematical Problems in Engineering 3 Inverse Problems in Science and Engineering 3 GEM - International Journal on Geomathematics 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Acta Applicandae Mathematicae 2 Applied Mathematics Letters 2 International Journal of Computer Mathematics 2 Communications in Numerical Methods in Engineering 2 Fractals 2 Nonlinear Analysis. Real World Applications 2 Central European Journal of Mathematics 2 International Journal of Wavelets, Multiresolution and Information Processing 2 International Journal of Computational Methods 2 Mediterranean Journal of Mathematics 1 Applicable Analysis 1 Biological Cybernetics 1 International Journal for Numerical Methods in Fluids 1 International Journal of Solids and Structures 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 The Mathematical Intelligencer 1 British Journal of Mathematical & Statistical Psychology 1 Computing 1 Journal of Approximation Theory 1 Journal of Optimization Theory and Applications 1 Mathematische Zeitschrift 1 Numerical Functional Analysis and Optimization 1 Results in Mathematics 1 Studies in Applied Mathematics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Constructive Approximation 1 Computational Mechanics 1 Numerical Methods for Partial Differential Equations 1 Mathematical and Computer Modelling 1 Computational Mathematics and Modeling 1 Multidimensional Systems and Signal Processing 1 The Annals of Applied Probability 1 Applications of Mathematics 1 Applied Mathematical Modelling 1 Journal of Statistical Computation and Simulation 1 Pattern Recognition 1 Journal of Mathematical Imaging and Vision 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Applied Mathematics. Series B (English Edition) 1 Applied and Computational Harmonic Analysis 1 Journal of Geodesy 1 Journal of Mathematical Chemistry 1 Nonlinear Dynamics 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 Journal of Applied Statistics 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Engineering Computations 1 Combustion Theory and Modelling 1 Journal of the Australian Mathematical Society 1 Mathematical Geology 1 Missouri Journal of Mathematical Sciences 1 Review of Derivatives Research 1 Journal of Function Spaces and Applications 1 International Journal of Parallel, Emergent and Distributed Systems 1 Statistical Methodology 1 Journal of Zhejiang University. Science A 1 Journal of Fixed Point Theory and Applications 1 Journal of Theoretical Biology 1 Journal of Fractal Geometry 1 Journal of Function Spaces 1 International Journal of Applied and Computational Mathematics
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#### Cited in 44 Fields

 184 Numerical analysis (65-XX) 76 Approximations and expansions (41-XX) 26 Partial differential equations (35-XX) 22 Fluid mechanics (76-XX) 17 Computer science (68-XX) 15 Statistics (62-XX) 13 Biology and other natural sciences (92-XX) 11 Measure and integration (28-XX) 10 Ordinary differential equations (34-XX) 9 Statistical mechanics, structure of matter (82-XX) 9 Information and communication theory, circuits (94-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Geophysics (86-XX) 6 Functional analysis (46-XX) 6 Convex and discrete geometry (52-XX) 6 Mechanics of deformable solids (74-XX) 5 Number theory (11-XX) 5 Functions of a complex variable (30-XX) 4 Special functions (33-XX) 4 Probability theory and stochastic processes (60-XX) 4 Operations research, mathematical programming (90-XX) 3 Operator theory (47-XX) 3 Differential geometry (53-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Potential theory (31-XX) 2 Integral transforms, operational calculus (44-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Quantum theory (81-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX)