Relevant bibliographies by topics / Randomized Numerical Linear Algebra

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  2. Dissertations / Theses
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Academic literature on the topic 'Randomized Numerical Linear Algebra'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Randomized Numerical Linear Algebra"

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Kannan, Ravindran, and Santosh Vempala. "Randomized algorithms in numerical linear algebra." Acta Numerica 26 (May 1, 2017): 95–135. http://dx.doi.org/10.1017/s0962492917000058.

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This survey provides an introduction to the use of randomization in the design of fast algorithms for numerical linear algebra. These algorithms typically examine only a subset of the input to solve basic problems approximately, including matrix multiplication, regression and low-rank approximation. The survey describes the key ideas and gives complete proofs of the main results in the field. A central unifying idea is sampling the columns (or rows) of a matrix according to their squared lengths.
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Martinsson, Per-Gunnar, and Joel A. Tropp. "Randomized numerical linear algebra: Foundations and algorithms." Acta Numerica 29 (May 2020): 403–572. http://dx.doi.org/10.1017/s0962492920000021.

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This survey describes probabilistic algorithms for linear algebraic computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problems. The paper treats both the theoretical foundations of the subject and practical computational issues.Topics include norm estimation, matrix approximation by sampling, structured and unstructured random embeddings, linear regression problems, low-rank approximation, subspace iteration and Krylov methods, error estimation and adaptivity, interpolatory and CUR factorizations, Nyst
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Dereziński, Michał, and Michael W. Mahoney. "Determinantal Point Processes in Randomized Numerical Linear Algebra." Notices of the American Mathematical Society 68, no. 01 (2021): 1. http://dx.doi.org/10.1090/noti2202.

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Lim, Lek-Heng, and Jonathan Weare. "Fast Randomized Iteration: Diffusion Monte Carlo through the Lens of Numerical Linear Algebra." SIAM Review 59, no. 3 (2017): 547–87. http://dx.doi.org/10.1137/15m1040827.

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Novak, Erich. "Optimal linear randomized methods for linear operators in Hilbert spaces." Journal of Complexity 8, no. 1 (1992): 22–36. http://dx.doi.org/10.1016/0885-064x(92)90032-7.

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Pan, Victor Y., and Guoliang Qian. "Randomized Preprocessing of Homogeneous Linear Systems of Equations." Linear Algebra and its Applications 432, no. 12 (2010): 3272–318. http://dx.doi.org/10.1016/j.laa.2010.01.023.

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Oymak, Samet, and Joel A. Tropp. "Universality laws for randomized dimension reduction, with applications." Information and Inference: A Journal of the IMA 7, no. 3 (2017): 337–446. http://dx.doi.org/10.1093/imaiai/iax011.

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Abstract Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain geometric features of the set. The question is how large the embedding dimension must be to ensure that randomized dimension reduction succeeds with high probability. This article studies a natural family of randomized dimension reduction maps and a large class of data s
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Liu, Yong, and Chuan-Qing Gu. "On greedy randomized block Kaczmarz method for consistent linear systems." Linear Algebra and its Applications 616 (May 2021): 178–200. http://dx.doi.org/10.1016/j.laa.2021.01.024.

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Rudi, Alessandro, Leonard Wossnig, Carlo Ciliberto, Andrea Rocchetto, Massimiliano Pontil, and Simone Severini. "Approximating Hamiltonian dynamics with the Nyström method." Quantum 4 (February 20, 2020): 234. http://dx.doi.org/10.22331/q-2020-02-20-234.

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Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation technique whose runtime scales polynomially in the number of qubits and the Frobenius norm of the Hamiltonian. As an immediate application, we show that sample based quantum simulation, a type of evolution where the Hamiltonian is a density matrix, can be efficiently classically simu
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Novak, Erich, and Henryk Woźniakowski. "Lower bounds for the complexity of linear functionals in the randomized setting." Journal of Complexity 27, no. 1 (2011): 1–22. http://dx.doi.org/10.1016/j.jco.2010.08.002.

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Dissertations / Theses on the topic "Randomized Numerical Linear Algebra"

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Musco, Cameron N. (Cameron Nicholas). "The power of randomized algorithms : from numerical linear algebra to biological systems." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/120424.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 323-347).<br>In this thesis we study simple, randomized algorithms from a dual perspective. The first part of the work considers how randomized methods can be used to accelerate the solution of core problems in numerical linear algebra. In particular, we give a randomized low-rank approximation algorithm for positive semidefinite matrices that runs in sublinear time, significantly improving
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Wilkerson, Owen Tanner. "Fast, Sparse Matrix Factorization and Matrix Algebra via Random Sampling for Integral Equation Formulations in Electromagnetics." UKnowledge, 2019. https://uknowledge.uky.edu/ece_etds/147.

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Many systems designed by electrical & computer engineers rely on electromagnetic (EM) signals to transmit, receive, and extract either information or energy. In many cases, these systems are large and complex. Their accurate, cost-effective design requires high-fidelity computer modeling of the underlying EM field/material interaction problem in order to find a design with acceptable system performance. This modeling is accomplished by projecting the governing Maxwell equations onto finite dimensional subspaces, which results in a large matrix equation representation (Zx = b) of the EM problem
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DiPaolo, Conner. "Randomized Algorithms for Preconditioner Selection with Applications to Kernel Regression." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/230.

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The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M-1A ||F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which suggests the quantity is im
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Balabanov, Oleg. "Randomized linear algebra for model order reduction." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/668906.

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Solutions to high-dimensional parameter-dependent problems are in great demand in the contemporary applied science and engineering. The standard approximation methods for parametric equations can require computational resources that are exponential in the dimension of the parameter space, which is typically refereed to as the curse of dimensionality. To break the curse of dimensionality one has to appeal to nonlinear methods that exploit the structure of the solution map, such as projection-based model order reduction methods. This thesis proposes novel methods based on randomized linear a
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Battles, Zachary. "Numerical linear algebra for continuous functions." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427900.

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Higham, N. J. "Nearness problems in numerical linear algebra." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374580.

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Zounon, Mawussi. "On numerical resilience in linear algebra." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0038/document.

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Comme la puissance de calcul des systèmes de calcul haute performance continue de croître, en utilisant un grand nombre de cœurs CPU ou d’unités de calcul spécialisées, les applications hautes performances destinées à la résolution des problèmes de très grande échelle sont de plus en plus sujettes à des pannes. En conséquence, la communauté de calcul haute performance a proposé de nombreuses contributions pour concevoir des applications tolérantes aux pannes. Cette étude porte sur une nouvelle classe d’algorithmes numériques de tolérance aux pannes au niveau de l’application qui ne nécessite p
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Kannan, Ramaseshan. "Numerical linear algebra problems in structural analysis." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/numerical-linear-algebra-problems-in-structural-analysis(7df0f708-fc12-4807-a1f5-215960d9c4d4).html.

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A range of numerical linear algebra problems that arise in finite element-based structural analysis are considered. These problems were encountered when implementing the finite element method in the software package Oasys GSA. We present novel solutions to these problems in the form of a new method for error detection, algorithms with superior numerical effeciency and algorithms with scalable performance on parallel computers. The solutions and their corresponding software implementations have been integrated into GSA's program code and we present results that demonstrate the use of these impl
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Gulliksson, Rebecka. "A comparison of parallelization approaches for numerical linear algebra." Thesis, Umeå universitet, Institutionen för datavetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-81116.

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The efficiency of numerical libraries for a given computation is highly dependent on the size of the inputs. For very small inputs it is expected that LAPACK combined with BLAS is the superior alternative, while the new generation of parallelized numerical libraries (such as PLASMA and SuperMatrix) is expected to be superior for large inputs. In between these two extremes in input sizes, there might exist a niche for a new class of numerical libraries.In this thesis a prototype library, targeting medium sized inputs, is presented. The prototype library uses a mixed data and task parallel appro
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Song, Zixu. "Software engineering abstractions for a numerical linear algebra library." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/software-engineering-abstractions-for-a-numerical-linear-algebra-library(68304a9b-56db-404b-8ffb-4613f5102c1a).html.

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This thesis aims at building a numerical linear algebra library with appropriate software engineering abstractions. Three areas of knowledge, namely, Numerical Linear Algebra (NLA), Software Engineering and Compiler Optimisation Techniques, are involved. Numerical simulation is widely used in a large number of distinct disciplines to help scientists understand and discover the world. The solutions to frequently occurring numerical problems have been implemented in subroutines, which were then grouped together to form libraries for ease of use. The design, implementation and maintenance of a NL
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Books on the topic "Randomized Numerical Linear Algebra"

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O, Christenson Charles, and Smith Bryan A, eds. Numerical linear algebra. BCS Associates, 1991.

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David, Bau, ed. Numerical linear algebra. Society for Industrial and Applied Mathematics, 1997.

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Numerical linear algebra. Springer, 2008.

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Bornemann, Folkmar. Numerical Linear Algebra. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74222-9.

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Reichel, Lothar, Arden Ruttan, and Richard S. Varga, eds. Numerical Linear Algebra. DE GRUYTER, 1993. http://dx.doi.org/10.1515/9783110857658.

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Allaire, Grégoire, and Sidi Mahmoud Kaber. Numerical Linear Algebra. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-68918-0.

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Hager, William W. Applied numerical linear algebra. Prentice-Hall, 1988.

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Applied numerical linear algebra. Society for Industrial and Applied Mathematics, 1997.

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Hager, William W. Applied numerical linear algebra. Prentice Hall International, 1988.

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Datta, Biswa Nath. Numerical linear algebra and applications. 2nd ed. Society for Industrial and Applied Mathematics, 2009.

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Book chapters on the topic "Randomized Numerical Linear Algebra"

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Robbiano, Lorenzo. "Numerical and Symbolic Computations." In Linear algebra. Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1839-6_1.

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Kalé, Laxmikant V., Abhinav Bhatele, Eric J. Bohm, et al. "Numerical Linear Algebra." In Encyclopedia of Parallel Computing. Springer US, 2011. http://dx.doi.org/10.1007/978-0-387-09766-4_2081.

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Dongarra, Jack, Piotr Luszczek, Paul Feautrier, et al. "Linear Algebra, Numerical." In Encyclopedia of Parallel Computing. Springer US, 2011. http://dx.doi.org/10.1007/978-0-387-09766-4_126.

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Gentle, James E. "Numerical Linear Algebra." In Statistics and Computing. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-98144-4_5.

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Gentle, James E. "Numerical Linear Algebra." In Springer Texts in Statistics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64867-5_11.

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Čížková, Lenka, and Pavel Čížek. "Numerical Linear Algebra." In Handbook of Computational Statistics. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21551-3_5.

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Khoury, Richard, and Douglas Wilhelm Harder. "Linear Algebra." In Numerical Methods and Modelling for Engineering. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-21176-3_4.

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Gatzke, Edward. "Linear Algebra." In Introduction to Modeling and Numerical Methods for Biomedical and Chemical Engineers. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76449-4_7.

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Higham, Nicholas J. "Testing linear algebra software." In Quality of Numerical Software. Springer US, 1997. http://dx.doi.org/10.1007/978-1-5041-2940-4_8.

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Gentle, James E. "Software for Numerical Linear Algebra." In Springer Texts in Statistics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64867-5_12.

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Conference papers on the topic "Randomized Numerical Linear Algebra"

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Valley, George C., Thomas J. Shaw, Andrew D. Stapleton, Adam C. Scofield, George A. Sefler, and Leif Johannson. "Application of laser speckle to randomized numerical linear algebra." In Optical Data Science: Trends Shaping the Future of Photonics, edited by Ken-ichi Kitayama, Bahram Jalali, and Ata Mahjoubfar. SPIE, 2018. http://dx.doi.org/10.1117/12.2294574.

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Clarkson, Kenneth L., and David P. Woodruff. "Numerical linear algebra in the streaming model." In the 41st annual ACM symposium. ACM Press, 2009. http://dx.doi.org/10.1145/1536414.1536445.

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Ammar, Gregory. "Grassmannians, Riccati equations, and numerical linear algebra." In 1985 24th IEEE Conference on Decision and Control. IEEE, 1985. http://dx.doi.org/10.1109/cdc.1985.268867.

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Meier, Ulrike, and Ahmed Sameh. "Numerical Linear Algebra On The CEDAR Multiprocessor." In 31st Annual Technical Symposium, edited by Franklin T. Luk. SPIE, 1988. http://dx.doi.org/10.1117/12.942008.

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Václavíková, Zuzana, and Ondřej Kolouch. "Linear algebra for students of informatics." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0027086.

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Georganas, Evangelos, Jorge Gonzalez-Dominguez, Edgar Solomonik, Yili Zheng, Juan Tourino, and Katherine Yelick. "Communication avoiding and overlapping for numerical linear algebra." In 2012 SC - International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE, 2012. http://dx.doi.org/10.1109/sc.2012.32.

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Krake, Tim. "Numerical Linear Algebra for physically-based Fluid Animations." In SA '19: SIGGRAPH Asia 2019. ACM, 2019. http://dx.doi.org/10.1145/3366344.3366445.

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Haddock, Jamie, and Deanna Needell. "Randomized projections for corrupted linear systems." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044141.

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Wu, Wenyuan, and Greg Reid. "Application of numerical algebraic geometry and numerical linear algebra to PDE." In the 2006 international symposium. ACM Press, 2006. http://dx.doi.org/10.1145/1145768.1145824.

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Escobar Acevedo, Marco Antonio, Julio C. Estrada, and Javier Vargas. "Linear algebra approach to phase shifting interferometry: numerical methods." In Applied Optical Metrology III, edited by Erik Novak and James D. Trolinger. SPIE, 2019. http://dx.doi.org/10.1117/12.2530125.

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Reports on the topic "Randomized Numerical Linear Algebra"

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Bradley, John S. Special Year on Numerical Linear Algebra. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada208199.

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Carson, E. Final Report: Mixed Precision Numerical Linear Algebra. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1798446.

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Georganas, Evangelos, Jorge Gonzalez-Dominguez, Edgar Solomonik, Yili Zheng, Juan Tourino, and Katherine A. Yelick. Communication Avoiding and Overlapping for Numerical Linear Algebra. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada561679.

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Vu, Van H. Random Matrices, Combinatorics, Numerical Linear Algebra and Complex Networks. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada567088.

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Demmel, James. Conference: Three Decades of Numerical Linear Algebra at Berkeley. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada264964.

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