Karl E. Gustafson

1.2k total citations
19 papers, 703 citations indexed

About

Karl E. Gustafson is a scholar working on Applied Mathematics, Mathematical Physics and Artificial Intelligence. According to data from OpenAlex, Karl E. Gustafson has authored 19 papers receiving a total of 703 indexed citations (citations by other indexed papers that have themselves been cited), including 6 papers in Applied Mathematics, 4 papers in Mathematical Physics and 4 papers in Artificial Intelligence. Recurrent topics in Karl E. Gustafson's work include Matrix Theory and Algorithms (4 papers), Algebraic and Geometric Analysis (4 papers) and Neural Networks and Applications (3 papers). Karl E. Gustafson is often cited by papers focused on Matrix Theory and Algorithms (4 papers), Algebraic and Geometric Analysis (4 papers) and Neural Networks and Applications (3 papers). Karl E. Gustafson collaborates with scholars based in United States and Belgium. Karl E. Gustafson's co-authors include Duggirala K. M. Rao, James A. Sethian, I. Αντωνίου, Brian Eaton, Robert K. Goodrich, Kristina M. Johnson, W. G. Pritchard, P. Freymuth, R. R. Leben and William P. Reinhardt and has published in prestigious journals such as Mathematics of Computation, Physica A Statistical Mechanics and its Applications and Chaos Solitons & Fractals.

In The Last Decade

Karl E. Gustafson

19 papers receiving 639 citations

Peers — A (Enhanced Table)

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

Name	h						Papers	Cites
Karl E. Gustafson United States	10	399	385	161	109	92	19	703
Hugo J. Woerdeman United States	16	333 0.8×	463 1.2×	146 0.9×	110 1.0×	67 0.7×	89	800
Ilya M. Spitkovsky United States	14	541 1.4×	459 1.2×	312 1.9×	213 2.0×	104 1.1×	125	866
J. P. Williams United States	14	529 1.3×	435 1.1×	400 2.5×	246 2.3×	63 0.7×	39	904
E. B. Saff United States	14	499 1.3×	150 0.4×	88 0.5×	79 0.7×	133 1.4×	58	782
Werner Balser Germany	13	368 0.9×	266 0.7×	166 1.0×	97 0.9×	313 3.4×	58	881
Deborah Tepper Haimo United States	13	411 1.0×	125 0.3×	243 1.5×	44 0.4×	65 0.7×	41	749
Harold S. Shapiro Sweden	18	709 1.8×	243 0.6×	351 2.2×	66 0.6×	227 2.5×	66	1.3k
Georgiĭ Evgenʹevich Shilov Israel	11	278 0.7×	142 0.4×	280 1.7×	101 0.9×	81 0.9×	29	700
János Bognár Hungary	2	259 0.6×	236 0.6×	336 2.1×	68 0.6×	78 0.8×	4	651
Paul Koosis Canada	12	686 1.7×	188 0.5×	416 2.6×	80 0.7×	166 1.8×	25	972

Countries citing papers authored by Karl E. Gustafson

Since Specialization

Citations

This map shows the geographic impact of Karl E. Gustafson'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 Karl E. Gustafson with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Karl E. Gustafson more than expected).

Fields of papers citing papers by Karl E. Gustafson

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Karl E. Gustafson. 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 Karl E. Gustafson. The network helps show where Karl E. Gustafson may publish in the future.

Co-authorship network of co-authors of Karl E. Gustafson

This figure shows the co-authorship network connecting the top 25 collaborators of Karl E. Gustafson. A scholar is included among the top collaborators of Karl E. Gustafson 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 Karl E. Gustafson. Karl E. Gustafson is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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19 of 19 papers shown

Gustafson, Karl E.. (2011). Antieigenvalue Analysis: With Applications to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance and Optimization. Medical Entomology and Zoology. 5 indexed citations

Gustafson, Karl E. & William P. Reinhardt. (2011). "Quantum Mechanics in Mathematics, Chemistry, and Physics". Medical Entomology and Zoology. 1 indexed citations

Gustafson, Karl E., et al.. (2005). On the eigenvalues which express antieigenvalues. International Journal of Mathematics and Mathematical Sciences. 2005(10). 1543–1554. 10 indexed citations

Gustafson, Karl E., et al.. (2002). An asymptotic singular value decomposition analysis of nonlinear multilayer neural networks. i. 785–789. 4 indexed citations

Αντωνίου, I. & Karl E. Gustafson. (2000). The Time operator of wavelets. Chaos Solitons & Fractals. 11(1-3). 443–452. 12 indexed citations

Gustafson, Karl E.. (1999). A COMPUTATIONAL TRIGONOMETRY, AND RELATED CONTRIBUTIONS BY RUSSIANS KANTOROVICH, KREIN, KAPORIN. 4(3). 3 indexed citations

Gustafson, Karl E.. (1997). Introduction to partial differential equations and Hilbert space methods. CERN Bulletin. 41 indexed citations

Gustafson, Karl E. & Duggirala K. M. Rao. (1997). Numerical Range. Universitext. 191 indexed citations

Gustafson, Karl E.. (1996). Numerical Range: The Field of Values of Linear Operators and Matrices. CERN Document Server (European Organization for Nuclear Research). 321 indexed citations

10.

Αντωνίου, I. & Karl E. Gustafson. (1993). From probabilistic descriptions to deterministic dynamics. Physica A Statistical Mechanics and its Applications. 197(1-2). 153–166. 11 indexed citations

11.

Pritchard, W. G., Karl E. Gustafson, & James A. Sethian. (1992). Vortex Methods and Vortex Motion.. Mathematics of Computation. 59(199). 302–302. 9 indexed citations

12.

Gustafson, Karl E. & James A. Sethian. (1991). Vortex Methods and Vortex Motion. Society for Industrial and Applied Mathematics eBooks. 49 indexed citations

13.

Freymuth, P., Karl E. Gustafson, & R. R. Leben. (1991). 6. Visualization and Computation of Hovering Mode Vortex Dynamics. Society for Industrial and Applied Mathematics eBooks. 143–169. 7 indexed citations

14.

Johnson, Kristina M., et al.. (1990). A Second-Order Translation, Rotation and Scale Invariant Neural Network. Neural Information Processing Systems. 3. 313–319. 3 indexed citations

15.

Gustafson, Karl E., et al.. (1990). Connectionist nonlinear over-relaxation. 179–184 vol.3. 1 indexed citations

16.

Goodrich, Robert K. & Karl E. Gustafson. (1986). Spectral Approximation. Journal of Approximation Theory. 48(3). 272–293. 4 indexed citations

17.

Gustafson, Karl E. & Brian Eaton. (1982). Exact solutions and ignition parameters in the Arrhenius conduction theory of gaseous thermal explosion. Zeitschrift für angewandte Mathematik und Physik. 33(3). 392–405. 14 indexed citations

18.

Goodrich, Robert K. & Karl E. Gustafson. (1981). Weighted trigonometric approximation and inner—Outer functions on higher dimensional Euclidean spaces. Journal of Approximation Theory. 31(4). 368–382. 2 indexed citations

19.

Gustafson, Karl E., et al.. (1973). Some essentially self-adjoint Dirac operators with spherically symmetric potentials. Israel Journal of Mathematics. 14(1). 63–75. 15 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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