Jane Grace Kehoe Cullum (born 1938) [1] is an American applied mathematician known for her work in numerical algorithms and control theory, who became president of the IEEE Control Systems Society.
Cullum studied chemical engineering at Virginia Tech, graduating in 1960. [2] [3] She continued at Virginia Tech for a master's degree in mathematics in 1962, with the master's thesis Applications of the analog computer to mathematical problems. [4] She completed a Ph.D. in applied mathematics at the University of California, Berkeley, in 1966. Her dissertation, Continuous Optimal Control Problems with Phase Space Constraints, concerned control theory, and was supervised by Stephen Diliberto. [5]
She worked for IBM Research at the Thomas J. Watson Research Center from 1967 until 1998, when she moved to the Los Alamos National Laboratory. [2]
She served as president of the IEEE Control Systems Society in 1989. [6]
With Ralph A. Willoughby, Cullum is the coauthor of the books Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Vol. I, Theory and Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Vol. II, Programs (Birkhäuser, 1985). [7] The first volume was reprinted by the Society for Industrial and Applied Mathematics in 2002, as volume 41 of their Classics in Applied Mathematics book series. [8]
The IEEE Control Systems Society gave Cullum their Distinguished Member Award in 1989. [6] She was elected as an IEEE Fellow in 1990, "for contributions to practical numerical algorithms for large-scale systems". [9]
Ronald Lewis Graham was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.
In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal, and the supradiagonal/upper diagonal. For example, the following matrix is tridiagonal:
Cornelius (Cornel) Lanczos was a Hungarian-Jewish, Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians.
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the "most useful" eigenvalues and eigenvectors of an Hermitian matrix, where is often but not necessarily much smaller than . Although computationally efficient in principle, the method as initially formulated was not useful, due to its numerical instability.
Eduardo Daniel Sontag is an Argentine-American mathematician, and distinguished university professor at Northeastern University, who works in the fields control theory, dynamical systems, systems molecular biology, cancer and immunology, theoretical computer science, neural networks, and computational biology.
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible.
In computational mathematics, a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix-vector products. Such methods can be preferable when the matrix is so big that storing and manipulating it would cost a lot of memory and computing time, even with the use of methods for sparse matrices. Many iterative methods allow for a matrix-free implementation, including:
Magnus B. Egerstedt is a Swedish-American roboticist who is the Dean of the Henry Samueli School of Engineering at the University of California, Irvine. He was formerly the Steve C. Chaddick School Chair and Professor at the School of Electrical and Computer Engineering, Georgia Institute of Technology.
Joseph O'Rourke is the Spencer T. and Ann W. Olin Professor of Computer Science at Smith College and the founding chair of the Smith computer science department. His main research interest is computational geometry.
Carol Lee Walker is a retired American mathematician and mathematics textbook author. Walker's early mathematical research, in the 1960s and 1970s, concerned the theory of abelian groups. In the 1990s, her interests shifted to fuzzy logic and fuzzy control systems.
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest eigenvalues and the corresponding eigenvectors of a symmetric generalized eigenvalue problem
The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.
Ruth F. Curtain was an Australian mathematician who worked for many years in the Netherlands as a professor of mathematics at the University of Groningen. Her research concerned infinite-dimensional linear systems.
Mariette Yvinec is a French researcher in computational geometry at the French Institute for Research in Computer Science and Automation (INRIA) in Sophia Antipolis. She is one of the developers of CGAL, a software library of computational geometry algorithms.
Lynn Margaret Batten was a Canadian-Australian mathematician known for her books about finite geometry and cryptography, and for her research on the classification of malware.
Fioralba Cakoni is an American-Albanian mathematician and an expert on inverse scattering theory. She is a professor of mathematics at Rutgers University.
Hazel Perfect was a British mathematician specialising in combinatorics.
Beresford Neill Parlett is an English applied mathematician, specializing in numerical analysis and scientific computation.
Algorithmic Geometry is a textbook on computational geometry. It was originally written in the French language by Jean-Daniel Boissonnat and Mariette Yvinec, and published as Géometrie algorithmique by Edusciences in 1995. It was translated into English by Hervé Brönnimann, with improvements to some proofs and additional exercises, and published by the Cambridge University Press in 1998.
Monique Chyba is a control theorist who works as a professor of mathematics at the University of Hawaiʻi at Mānoa. Her work on control theory has involved the theory of singular trajectories, and applications in the control of autonomous underwater vehicles. More recently, she has also applied control theory to the prediction and modeling of the spread of COVID-19 in Hawaii.
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