|
Showing 1 - 4 of
4 matches in All Departments
This user-friendly, engaging textbook makes the material accessible
to graduate students and new researchers who wish to study the
rapidly exploding area of computations with structured matrices and
polynomials. The book goes beyond research frontiers and, apart
from very recent research articles, includes previously unpublished
results.
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.
Structured matrices serve as a natural bridge between the areas of
algebraic computations with polynomials and numerical matrix
computations, allowing cross-fertilization of both fields. This
book covers most fundamental numerical and algebraic computations
with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular
structured matrices. Throughout the computations, the matrices are
represented by their compressed images, called displacements,
enabling both a unified treatment of various matrix structures and
dramatic saving of computer time and memory. The resulting
superfast algorithms allow further dramatic parallel acceleration
using FFT and fast sine and cosine transforms. Included are
specific applications to other fields, in particular, superfast
solutions to: various fundamental problems of computer algebra; the
tangential Nevanlinna--Pick and matrix Nehari problems The primary
intended readership for this work includes researchers, algorithm
designers, and advanced graduate students in the fields of
computations with structured matrices, computer algebra, and
numerical rational interpolation. The book goes beyond research
frontiers and, apart from very recent research articles, includes
yet unpublished results. To serve a wider audience, the
presentation unfolds systematically and is written in a
user-friendly engaging style. Only some preliminary knowledge of
the fundamentals of linear algebra is required. This makes the
material accessible to graduate students and new researchers who
wish to study the rapidly exploding area of computations with
structured matrices and polynomials. Examples, tables, figures,
exercises, extensive bibliography, and index lend this text
toclassroom use or self-study.
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.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|