Werner C. Rheinboldt

University of Pittsburgh

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James M. Ortega

Peruvian University of Applied Sciences

Patrick J. Rabier

University of Pittsburgh

Ivo Babuška

The University of Texas at Austin

C. K. Mesztenyi

University of Maryland, College Park

James P. Fink

University of Pittsburgh

John Burkardt

University of Pittsburgh

John W. Hamblen

Missouri University of Science and Technology

James S. Vandergraft

Coleman University

Silvio O. Navarro

University of Kentucky

David M. Young

Holistic Management International

Cooperative Institutions

University of Maryland, College Park

University of Pittsburgh

Stanford University

Purdue University West Lafayette

University of Chicago

Princeton University

University of California, Berkeley

Applied Mathematics (United States)

Oak Ridge National Laboratory

The University of Texas at Austin

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Introduction to Algol

Werner C. Rheinboldt Rüdeger Baumann M. Feliciano Friedrich L. Bauer K. Samuelsoon

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Citations (13)

The CUPM recommendations on a computational mathematics program and on the impact of computers on undergraduate mathematics courses

ACM SIGCSE Bulletin (1973)

Werner C. Rheinboldt

The growing influence of modern electronic computing in many fields of knowledge has contributed to a dramatic increase and diversification in the application of mathematics to other disciplines. No longer are the uses of mathematics confined exclusively to the physical sciences and engineering; they are found with increasing frequency in the social, behavioral, and life sciences as well. At the same time the use of the computer has led to different requirements for the solution process in mathematics itself. Theory construction and model building have assumed a different dimension; in addition to knowing existence theorems, the user of mathematics must know constructive methods for solving problems, and he must have the means to ascertain the efficiency as well as the correctness of these methods.

Constructive

10.1145/953053.808084

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The Role of the Tangent Mapping in Analyzing Bifurcation Behaviour

De Gruyter eBooks (1984)

J. P. Fink Werner C. Rheinboldt

10.1515/9783112554449-005

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Continuation Techniques and Bifurcation Problems.

Mathematics of Computation (1991)

Werner C. Rheinboldt Hans D. Mittelmann Dirk Roose

Continuation

10.2307/2008554

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8. Unconstrained Minimization Methods

Society for Industrial and Applied Mathematics eBooks (1998)

Werner C. Rheinboldt

As we observed, the problem of solving a system of nonlinear equations may be replaced by a problem of minimizing a nonlinear functional on Rn . The literature in this area is extensive; see, e.g., the books by Fletcher [96], Gill, Murray, and Wright [109], and Dennis and Schnabel [66], as well as the bibliography by Berman [23]. We present here only a very modest introduction to some convergence theory for a few classes of methods for solving unconstrained minimization problems.

Generality

Minification

Wright

Simplicity

10.1137/1.9781611970012.ch8

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Adaptive mesh refinement processes for finite element solutions

International Journal for Numerical Methods in Engineering (1981)

Werner C. Rheinboldt

Abstract The nature of adaptive processes is reviewed using as an example a specific finite element problem. Several possible formulations for the objective of mesh refinement processes are given. For the most natural of these objectives the A *‐algorithms of artificial intelligence turn out to provide a solution process which is known to be optimal in a certain sense. But practically, there is insufficient information and these processes tend to be inefficient. On the other hand, if the objective is replaced by a strictly local objective based on Pareto‐optimality, the error estimates of the resulting mesh sequence are shown to exhibit the order of convergence which is known to be best possible for the type of elements used.

Sequence (biology)

Adaptive Mesh Refinement

Pareto optimal

10.1002/nme.1620170502

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Citations (45)

On a programming language for graph algorithms

BIT Numerical Mathematics (1972)

Werner C. Rheinboldt Victor R. Basilli C. K. Mesztenyi

Graph algebra

Null graph

Morphism

Graph property

10.1007/bf01932817

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Citations (21)

Pathways to Solutions, Fixed Points, and Equilibria. By C. B. Garcia and W. I. Zangwill

American Mathematical Monthly (1983)

Werner C. Rheinboldt

"Pathways to Solutions, Fixed Points, and Equilibria. By C. B. Garcia and W. I. Zangwill." The American Mathematical Monthly, 90(1), pp. 66–67

Garcia

10.1080/00029890.1983.11971159

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A Posteriori Error Estimates for Parametrized Nonlinear Equations

Werner C. Rheinboldt Jinn-Lian Liu

Abstract : A new approach to the construction of a posteriori error estimates for finite element solutions of multiparameter nonlinear problems presented. The estimates are derived from local, element-by-element solutions of linearizations of the problems; they turn out to be very effective, computationally rather inexpensive, and insensitive to the choice of the local coordinate system on the solution manifold. Frequently, in practical computations in engineering and science, the aim is to obtain results which are sufficiently accurate and reliable to allow for a decision about the physical system under study. A posteriori error estimates play a very important role in achieving this aim. Such estimates are needed not only for judging the reliability of the computed results but also for controlling adaptive processes designed to achieve desired error tolerances at minimal cost or best possible solutions within allowable cost ranges. (KR)

Manifold (fluid mechanics)

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Zur äußeren Randbedingung bei den Grenzschichtgleichungen .

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (1956)

Werner C. Rheinboldt

10.1002/zamm.19560360315

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Citations (5)