Werner C. Rheinboldt

25.2k total citations · 6 hit papers
132 papers, 15.7k citations indexed

About

Werner C. Rheinboldt is a scholar working on Computational Theory and Mathematics, Numerical Analysis and Computational Mechanics. According to data from OpenAlex, Werner C. Rheinboldt has authored 132 papers receiving a total of 15.7k indexed citations (citations by other indexed papers that have themselves been cited), including 57 papers in Computational Theory and Mathematics, 55 papers in Numerical Analysis and 42 papers in Computational Mechanics. Recurrent topics in Werner C. Rheinboldt's work include Numerical methods for differential equations (35 papers), Matrix Theory and Algorithms (34 papers) and Advanced Numerical Methods in Computational Mathematics (31 papers). Werner C. Rheinboldt is often cited by papers focused on Numerical methods for differential equations (35 papers), Matrix Theory and Algorithms (34 papers) and Advanced Numerical Methods in Computational Mathematics (31 papers). Werner C. Rheinboldt collaborates with scholars based in United States, Germany and Canada. Werner C. Rheinboldt's co-authors include Ivo Babuška, L. J. Slater, J.A. Abildskov, Gordon K. Moe, Patrick J. Rabier, John Burkardt, J. L. Synge, Alexander B. Morgan, James P. Fink and James M. Ortega and has published in prestigious journals such as Physics Today, Communications of the ACM and Computer Methods in Applied Mechanics and Engineering.

In The Last Decade

Werner C. Rheinboldt

129 papers receiving 13.8k citations

Hit Papers

5 papers align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Iterative Solution of Nonlinear Equations in Several Variables

1971 3.3k citations Werner C. Rheinboldt et al. Mathematics of Computation profile →
Iterative Solution of Nonlinear Equations in Several Variables

2000 3.0k citations Werner C. Rheinboldt et al. Society for Industrial and Applied Mathematics eBooks profile →
Generalized Hypergeometric Functions

1967 1.1k citations Werner C. Rheinboldt et al. profile →
Error Estimates for Adaptive Finite Element Computations

1978 1.0k citations Werner C. Rheinboldt et al. profile →
A computer model of atrial fibrillation

1964 959 citations Werner C. Rheinboldt et al. profile →
A‐posteriori error estimates for the finite element method

1978 866 citations Werner C. Rheinboldt et al. profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
Werner C. Rheinboldt United States	45	5.7k	5.3k	4.4k	1.9k	1.5k	132	15.7k
Lloyd N. Trefethen United Kingdom	54	3.8k 0.7×	3.9k 0.7×	5.4k 1.2×	1.4k 0.7×	2.1k 1.4×	175	17.4k
Herbert B. Keller United States	45	2.6k 0.5×	2.0k 0.4×	3.6k 0.8×	1.1k 0.6×	812 0.5×	130	9.9k
Gilbert Strang United States	43	2.0k 0.3×	3.0k 0.6×	5.0k 1.1×	3.0k 1.6×	2.1k 1.4×	185	18.6k
M. J. D. Powell United Kingdom	41	4.0k 0.7×	3.9k 0.7×	2.7k 0.6×	1.0k 0.5×	1.5k 1.0×	101	17.5k
Carl de Boor United States	41	2.3k 0.4×	1.9k 0.4×	6.3k 1.5×	1.4k 0.7×	795 0.5×	156	16.4k
L. F. Shampine United States	45	3.8k 0.7×	1.8k 0.3×	3.1k 0.7×	741 0.4×	1.8k 1.2×	187	12.5k
Peter Lancaster Canada	36	2.2k 0.4×	3.8k 0.7×	1.5k 0.4×	2.2k 1.1×	955 0.6×	184	10.3k
J. E. Dennis United States	40	4.9k 0.9×	6.8k 1.3×	2.4k 0.5×	712 0.4×	1.6k 1.1×	86	18.0k
Max Gunzburger United States	65	1.8k 0.3×	3.4k 0.6×	7.9k 1.8×	3.5k 1.8×	1.9k 1.2×	333	14.9k
Ernst Hairer Switzerland	42	10.3k 1.8×	4.2k 0.8×	6.5k 1.5×	684 0.4×	3.4k 2.2×	119	17.1k

Countries citing papers authored by Werner C. Rheinboldt

Since Specialization

Citations

This map shows the geographic impact of Werner C. Rheinboldt's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Werner C. Rheinboldt with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Werner C. Rheinboldt more than expected).

Fields of papers citing papers by Werner C. Rheinboldt

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Werner C. Rheinboldt. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Werner C. Rheinboldt. The network helps show where Werner C. Rheinboldt may publish in the future.

Co-authorship network of co-authors of Werner C. Rheinboldt

This figure shows the co-authorship network connecting the top 25 collaborators of Werner C. Rheinboldt. A scholar is included among the top collaborators of Werner C. Rheinboldt based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Werner C. Rheinboldt. Werner C. Rheinboldt is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

Sort: Min cites: Since: Top N: Style:

20 of 20 papers shown

Rheinboldt, Werner C.. (2000). Numerical continuation methods: a perspective. Journal of Computational and Applied Mathematics. 124(1-2). 229–244. 22 indexed citations

Rheinboldt, Werner C. & Bernd Simeon. (1999). Computing smooth solutions of DAEs for elastic multibody systems. Computers & Mathematics with Applications. 37(6). 69–83. 3 indexed citations

Rabier, Patrick J. & Werner C. Rheinboldt. (1996). Time-dependent linear DAEs with discontinuous inputs. Linear Algebra and its Applications. 247. 1–29. 17 indexed citations

Rabier, Patrick J. & Werner C. Rheinboldt. (1996). Classical and generalized solutions of time-dependent linear differential-algebraic equations. Linear Algebra and its Applications. 245. 259–293. 37 indexed citations

Rheinboldt, Werner C. & Bernd Simeon. (1995). Performance analysis of some methods for solving Euler-Lagrange equations. Applied Mathematics Letters. 8(1). 77–82. 9 indexed citations

Rabier, Patrick J. & Werner C. Rheinboldt. (1994). On Impasse Points of Quasilinear Differential-Algebraic Equations. Journal of Mathematical Analysis and Applications. 181(2). 429–454. 63 indexed citations

Rabier, Patrick J. & Werner C. Rheinboldt. (1994). A Geometric Treatment of Implicit Differential-Algebraic Equations. Journal of Differential Equations. 109(1). 110–146. 81 indexed citations

Rabier, Patrick J. & Werner C. Rheinboldt. (1991). A general existence and uniqueness theory for implicit differential-algebraic equations. Differential and Integral Equations. 4(3). 24 indexed citations

Rheinboldt, Werner C.. (1984). Differential-algebraic systems as differential equations on manifolds. Mathematics of Computation. 43(168). 473–482. 125 indexed citations

10.

Rheinboldt, Werner C.. (1984). Differential-Algebraic Systems as Differential Equations on Manifolds. Mathematics of Computation. 43(168). 473–473. 15 indexed citations

11.

Rheinboldt, Werner C.. (1984). Error Estimations and Adaptive Techniques for Nonlinearized Parametrized Equations.. Defense Technical Information Center (DTIC). 1 indexed citations

12.

Rheinboldt, Werner C. & John Burkardt. (1981). A Program for a Locally-Parametrized Continuation Process.. Defense Technical Information Center (DTIC). 2 indexed citations

13.

Rheinboldt, Werner C.. (1976). On measures of ill-conditioning for nonlinear equations. Mathematics of Computation. 30(133). 104–111. 9 indexed citations

14.

Rheinboldt, Werner C. & James S. Vandergraft. (1973). A Simple Approach to the Perron-Frobenius Theory for Positive Operators on General Partially-Ordered Finite-Dimensional Linear Spaces. Mathematics of Computation. 27(121). 139–139. 7 indexed citations

15.

Morè, Jorge J. & Werner C. Rheinboldt. (1973). On P- and S-functions and related classes of n-dimensional nonlinear mappings. Linear Algebra and its Applications. 6. 45–68. 127 indexed citations

16.

Ortega, James M. & Werner C. Rheinboldt. (1970). Numerical solutions of nonlinear problems : a collection of papers. Society for Industrial and Applied Mathematics eBooks. 4 indexed citations

17.

Rheinboldt, Werner C.. (1970). On M-functions and their application to nonlinear Gauss-Seidel iterations and to network flows. Journal of Mathematical Analysis and Applications. 32(2). 274–307. 86 indexed citations

18.

Rheinboldt, Werner C.. (1969). Local Mapping Relations and Global Implicit Function Theorems. Transactions of the American Mathematical Society. 138. 183–183. 4 indexed citations

19.

Rheinboldt, Werner C.. (1969). Local mapping relations and global implicit function theorems. Transactions of the American Mathematical Society. 138(0). 183–198. 53 indexed citations

20.

Greub, Werner & Werner C. Rheinboldt. (1959). On a generalization of an inequality of L. V. Kantorovich. Proceedings of the American Mathematical Society. 10(3). 407–415. 77 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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