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Our Subjects and Objectives. This book is about algebraic and
symbolic computation and numerical computing (with matrices and
polynomials). It greatly extends the study of these topics
presented in the celebrated books of the seventies, [AHU] and [BM]
(these topics have been under-represented in [CLR], which is a
highly successful extension and updating of [AHU] otherwise).
Compared to [AHU] and [BM] our volume adds extensive material on
parallel com putations with general matrices and polynomials, on
the bit-complexity of arithmetic computations (including some
recent techniques of data compres sion and the study of numerical
approximation properties of polynomial and matrix algorithms), and
on computations with Toeplitz matrices and other dense structured
matrices. The latter subject should attract people working in
numerous areas of application (in particular, coding, signal
processing, control, algebraic computing and partial differential
equations). The au thors' teaching experience at the Graduate
Center of the City University of New York and at the University of
Pisa suggests that the book may serve as a text for advanced
graduate students in mathematics and computer science who have some
knowledge of algorithm design and wish to enter the exciting area
of algebraic and numerical computing. The potential readership may
also include algorithm and software designers and researchers
specializing in the design and analysis of algorithms,
computational complexity, alge braic and symbolic computing, and
numerical computation.
Our Subjects and Objectives. This book is about algebraic and
symbolic computation and numerical computing (with matrices and
polynomials). It greatly extends the study of these topics
presented in the celebrated books of the seventies, [AHU] and [BM]
(these topics have been under-represented in [CLR], which is a
highly successful extension and updating of [AHU] otherwise).
Compared to [AHU] and [BM] our volume adds extensive material on
parallel com putations with general matrices and polynomials, on
the bit-complexity of arithmetic computations (including some
recent techniques of data compres sion and the study of numerical
approximation properties of polynomial and matrix algorithms), and
on computations with Toeplitz matrices and other dense structured
matrices. The latter subject should attract people working in
numerous areas of application (in particular, coding, signal
processing, control, algebraic computing and partial differential
equations). The au thors' teaching experience at the Graduate
Center of the City University of New York and at the University of
Pisa suggests that the book may serve as a text for advanced
graduate students in mathematics and computer science who have some
knowledge of algorithm design and wish to enter the exciting area
of algebraic and numerical computing. The potential readership may
also include algorithm and software designers and researchers
specializing in the design and analysis of algorithms,
computational complexity, alge braic and symbolic computing, and
numerical computation.
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.
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