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Focusing on special matrices and matrices which are in some sense
`near' to structured matrices, this volume covers a broad range of
topics of current interest in numerical linear algebra.
Exploitation of these less obvious structural properties can be of
great importance in the design of efficient numerical methods, for
example algorithms for matrices with low-rank block structure,
matrices with decay, and structured tensor computations.
Applications range from quantum chemistry to queuing theory.
Structured matrices arise frequently in applications. Examples
include banded and sparse matrices, Toeplitz-type matrices, and
matrices with semi-separable or quasi-separable structure, as well
as Hamiltonian and symplectic matrices. The associated literature
is enormous, and many efficient algorithms have been developed for
solving problems involving such matrices. The text arose from a
C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to
present this fast growing field to young researchers, exploiting
the expertise of five leading lecturers with different theoretical
and application perspectives.
The most comprehensive treatment of FFTs to date. Van Loan captures
the interplay between mathematics and the design of effective
numerical algorithms--a critical connection as more advanced
machines become available. A stylized Matlab notation, which is
familiar to those engaged in high-performance computing, is used.
The Fast Fourier Transform (FFT) family of algorithms has
revolutionized many areas of scientific computation. The FFT is one
of the most widely used algorithms in science and engineering, with
applications in almost every discipline. This volume is essential
for professionals interested in linear algebra as well as those
working with numerical methods. The FFT is also a great vehicle for
teaching key aspects of scientific computing.
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