G.W. Stewart: Selected Works with Commentaries by Iain S. Duff (auth.), Misha E. Kilmer, Dianne P. O'Leary

By Iain S. Duff (auth.), Misha E. Kilmer, Dianne P. O'Leary (eds.)

Published in honor of his seventieth birthday, this quantity explores and celebrates the paintings of G.W. (Pete) Stewart, a world-renowned professional in computational linear algebra. it truly is greatly permitted that Stewart is the successor to James Wilkinson, the 1st massive within the box, taking on the perturbation idea learn that Wilkinson so ably begun and utilizing it as a starting place for algorithmic insights.

Stewart’s effects on rounding blunders in numerical computations supplied uncomplicated knowing of floating-point computation. His effects on perturbation of eigensystems, pseudo-inverses, least-squares difficulties, and matrix factorizations are primary to numerical perform this present day. His algorithms for the singular worth decomposition, updating and downdating matrix factorizations, and the eigenproblem broke new flooring and are nonetheless universal in more and more functions. Stewart’s papers, largely pointed out, are characterised by way of attractiveness in theorems and algorithms and transparent, concise, and gorgeous exposition. His six renowned textbooks are first-class assets of data and background. Stewart is a member of the nationwide Academy of Engineering and has obtained various extra honors, together with the Bauer Prize.

Key beneficial properties of this quantity include:

* Forty-four of Stewart’s so much influential examine papers in topic components: matrix algorithms and rounding and perturbation theory

* A biography of Stewart

* an entire record of Stewart’s guides, scholars, and honors

* chosen photographs

* Commentaries on Stewart’s works in collaboration with major specialists within the field

G.W. Stewart: chosen Works with Commentaries will attract graduate scholars, practitioners, and researchers in computational linear algebra and the historical past of mathematics.

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Additional info for G.W. Stewart: Selected Works with Commentaries

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Stewart’s paper [GWS-J94] succeeds in providing just that sort of insight. 4. Solving Sylvester Equations Other sections of this commentary discuss some of Stewart’s very clever algorithmic insights into problems such as storing plane rotations (Sect. 1), updating matrix factorizations (Chap. 5), and computing eigensystems (Chap. 8). W. Stewart for solving Sylvester equations [GWS-J17] is yet another illustration of the key role played by the ability to recognize exploitable structure. 1) for X, where the matrices are real valued, A is m×m, B is n×n, and C is m×n.

The scalar δ ∈ {+1, −1} is chosen to maximize δ − f T z− ukk + UT 13 z− + γg 1 . The first term encourages growth in the kth component of z, while the second term is a heuristic way of encouraging the emergence of “big numerators” during the subsequent computation of δk+1 , . . , δn . Experimental evidence affirms that the method is reliable. Condition estimators based on the ideas set forth in this paper were incorporated in Linpack [GWS-B2] and subsequently Lapack [1]. , [160]). , [83]). Condition estimation is now an integral part of numerical linear algebra computations, and it all started with this seminal contribution and the inclusion of the method in Linpack.

Major Honors of G. W. Stewart • • • • • The F. L. Bauer prize, awarded by the Technical University of Munich, 1998. Elected to the National Academy of Engineering, 2004. Distinguished University Professor, University of Maryland, 2006. Distinguished Editor of Linear Algebra and its Applications. SIAM Fellow (inaugural group), 2009. 3. D. Students of G. W. Stewart • • • • • • Eric Hill, “Computer Solution of Large Dense Linear Problems,” 1977. Nancy David, “A First Order Theory of Hypothesis Testing,” 1982.

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