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This IMA Volume in Mathematics and its Applications RECENT ADVANCES
IN ITERATIVE METHODS is based on the proceedings of a workshop that
was an integral part of the 1991-92 IMA program on "Applied Linear
Algebra. " Large systems of matrix equations arise frequently in
applications and they have the prop erty that they are sparse
and/or structured. The purpose of this workshop was to bring
together researchers in numerical analysis and various ap plication
areas to discuss where such problems arise and possible meth ods of
solution. The last two days of the meeting were a celebration
dedicated to Gene Golub on the occasion of his sixtieth birthday,
with the program arranged by Jack Dongarra and Paul van Dooren. We
are grateful to Richard Brualdi, George Cybenko, Alan George, Gene
Golub, Mitchell Luskin, and Paul Van Dooren for planning and
implementing the year-long program. We especially thank Gene Golub,
Anne Greenbaum, and Mitchell Luskin for organizing this workshop
and editing the proceed ings. The financial support of the National
Science Foundation and the Min nesota Supercomputer Institute made
the workshop possible. A vner Friedman Willard Miller, Jr. xi
PREFACE The solution of very large linear algebra problems is an
integral part of many scientific computations."
Numerical Methods provides a clear and concise exploration of
standard numerical analysis topics, as well as nontraditional ones,
including mathematical modeling, Monte Carlo methods, Markov
chains, and fractals. Filled with appealing examples that will
motivate students, the textbook considers modern application areas,
such as information retrieval and animation, and classical topics
from physics and engineering. Exercises use MATLAB and promote
understanding of computational results. The book gives instructors
the flexibility to emphasize different aspects--design, analysis,
or computer implementation--of numerical algorithms, depending on
the background and interests of students. Designed for
upper-division undergraduates in mathematics or computer science
classes, the textbook assumes that students have prior knowledge of
linear algebra and calculus, although these topics are reviewed in
the text. Short discussions of the history of numerical methods are
interspersed throughout the chapters. The book also includes
polynomial interpolation at Chebyshev points, use of the MATLAB
package Chebfun, and a section on the fast Fourier transform.
Supplementary materials are available online. * Clear and concise
exposition of standard numerical analysis topics * Explores
nontraditional topics, such as mathematical modeling and Monte
Carlo methods * Covers modern applications, including information
retrieval and animation, and classical applications from physics
and engineering * Promotes understanding of computational results
through MATLAB exercises * Provides flexibility so instructors can
emphasize mathematical or applied/computational aspects of
numerical methods or a combination * Includes recent results on
polynomial interpolation at Chebyshev points and use of the MATLAB
package Chebfun * Short discussions of the history of numerical
methods interspersed throughout * Supplementary materials available
online
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