Nicholas J. Higham's Books

Functions of Matrices

Theory and Computation

By: Nicholas J. Higham

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Functions of Matrices

Theory and Computation

By: Nicholas J. Higham

A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.

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Page Count

445

Publisher

SIAM

Published Date

ISBN 10

0898717779

ISBN 13

9780898717778

Handbook of Writing for the Mathematical Sciences

Third Edition

By: Nicholas J. Higham

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Handbook of Writing for the Mathematical Sciences

Third Edition

By: Nicholas J. Higham

Handbook of Writing for the Mathematical Sciences provides advice on all aspects of scientific writing, with a particular focus on writing mathematics. Its readable style and handy format, coupled with an extensive bibliography and comprehensive index, make it useful for everyone from undergraduates to seasoned professionals. This third edition revises, updates, and expands the best-selling second edition to reflect modern writing and publishing practices and builds on the author's extensive experience in writing and speaking about mathematics. Some of its key features include coverage of fundamentals of writing, including English usage, revising a draft, and writing when your first language is not English; thorough treatment of mathematical writing, including how to choose notation, how to choose between words and symbols, and how to format equations; and many tips for exploiting LaTeX and BibTeX. Higham also provides advice on how to write and publish a paper, covering the entire publication process, and includes anecdotes, quotes, and unusual facts that enliven the presentation. The new edition has been reorganized to make the book easier to use for reference; treats modern developments in publishing such as open access, DOIs, and ORCID; and contains more on poster design, including e-posters and the poster blitz. The new edition also includes five new chapters on the following topics: · workflow covering text editors, markup languages, version control, and much more; · the principles of indexing and how to prepare an index in LaTeX; · reviewing a paper, book proposal, or book; · writing a book, including advice on choosing a publisher and LaTeX tips particular to books; and · writing a blog post.

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Page Count

376

Publisher

SIAM

Published Date

ISBN 10

1611976103

ISBN 13

9781611976106

MATLAB Guide

Third Edition

By: Desmond J. Higham,Nicholas J. Higham

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MATLAB Guide

Third Edition

By: Desmond J. Higham,Nicholas J. Higham

MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools. This third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 30 percent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox. Key features are a tutorial in Chapter 1 that gives a hands-on overview of MATLAB; a thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers; and a web page at http://www.siam.org/books/ot150 that provides example program files, updates, and links to MATLAB resources. The new edition contains color figures throughout; includes pithy discussions of related topics in new ?Asides" boxes that augment the text; has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets; covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables; contains more on MATLAB workflow, including the Live Editor and unit tests; and fully reflects major updates to the MATLAB graphics system. This book is suitable for both beginners and more experienced users, including students, researchers, and practitioners.

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485

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SIAM

Published Date

ISBN 10

1611974666

ISBN 13

9781611974669

Accuracy and Stability of Numerical Algorithms

Second Edition

By: Nicholas J. Higham

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Accuracy and Stability of Numerical Algorithms

Second Edition

By: Nicholas J. Higham

Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

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Page Count

690

Publisher

SIAM

Published Date

ISBN 10

0898715210

ISBN 13

9780898715217

The Anglo-Saxon World

By: Nicholas J. Higham,M. J. Ryan

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The Anglo-Saxon World

By: Nicholas J. Higham,M. J. Ryan

Presents the Anglo-Saxon period of English history from the fifth century up to the late eleventh century, covering such events as the spread of Christianity, the invasions of the Vikings, the composition of Beowulf, and the Battle of Hastings.

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Page Count

495

Publisher

Yale University Press

Published Date

ISBN 10

0300125348

ISBN 13

9780300125344

King Arthur

The Making of the Legend

By: Nicholas J. Higham

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King Arthur

The Making of the Legend

By: Nicholas J. Higham

“A leading medievalist takes a clear-eyed look at the evidence for the existence of the legendary Arthur.” —The Sunday Times “Best Paperbacks of 2021” According to legend, King Arthur saved Britain from the Saxons and reigned over it gloriously sometime around A.D. 500. Whether or not there was a “real” King Arthur has all too often been neglected by scholars; most period specialists today declare themselves agnostic on this important matter. In this erudite volume, Nick Higham sets out to solve the puzzle, drawing on his original research and expertise to determine precisely when, and why, the legend began. Higham surveys all the major attempts to prove the origins of Arthur, weighing up and debunking hitherto claimed connections with classical Greece, Roman Dalmatia, Sarmatia, and the Caucasus. He then explores Arthur’s emergence in Wales—up to his rise to fame at the hands of Geoffrey of Monmouth. Certain to arouse heated debate among those committed to defending any particular Arthur, Higham’s book is an essential study for anyone seeking to understand how Arthur’s story began. “Likely to be the definitive text on the legendary warrior for the foreseeable future. With his profound knowledge of the rules of historical narrative and patient but forensic analysis of the evidence, Higham’s riveting book brings the historical Arthur to what may be his last, decisive battle.” —Max Adams, author of The First Kingdom “Fascinating, authoritative analysis.” —P. D. Smith, The Guardian “Intelligent and eminently readable . . . For fans of a fascinating story that is wonderfully well told, this is the perfect book to take you back to King Arthur’s time.” —All About History

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Page Count

339

Publisher

Yale University Press

Published Date

ISBN 10

0300240864

ISBN 13

9780300240863

Accuracy and Stability of Numerical Algorithms

Second Edition

By: Nicholas J. Higham

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Accuracy and Stability of Numerical Algorithms

Second Edition

By: Nicholas J. Higham

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Solve jigsaw puzzle

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Page Count

690

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SIAM

Published Date

ISBN 10

0898715210

ISBN 13

9780898715217

Functions of Matrices

Theory and Computation

By: Nicholas J. Higham

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Functions of Matrices

Theory and Computation

By: Nicholas J. Higham

“This superb book is timely and is written with great attention paid to detail, particularly in its referencing of the literature. The book has a wonderful blend of theory and code (MATLAB®) so will be useful both to nonexperts and to experts in the field.” — Alan Laub, Professor, University of California, Los Angeles The only book devoted exclusively to matrix functions, this research monograph gives a thorough treatment of the theory of matrix functions and numerical methods for computing them. The author's elegant presentation focuses on the equivalent definitions of f(A) via the Jordan canonical form, polynomial interpolation, and the Cauchy integral formula, and features an emphasis on results of practical interest and an extensive collection of problems and solutions. Functions of Matrices: Theory and Computation is more than just a monograph on matrix functions; its wide-ranging content—including an overview of applications, historical references, and miscellaneous results, tricks, and techniques with an f(A) connection—makes it useful as a general reference in numerical linear algebra.Other key features of the book include development of the theory of conditioning and properties of the Fréchet derivative; an emphasis on the Schur decomposition, the block Parlett recurrence, and judicious use of Padé approximants; the inclusion of new, unpublished research results and improved algorithms; a chapter devoted to the f(A)b problem; and a MATLAB® toolbox providing implementations of the key algorithms.Audience: This book is for specialists in numerical analysis and applied linear algebra as well as anyone wishing to learn about the theory of matrix functions and state of the art methods for computing them. It can be used for a graduate-level course on functions of matrices and is a suitable reference for an advanced course on applied or numerical linear algebra. It is also particularly well suited for self-study. Contents: List of Figures; List of Tables; Preface; Chapter 1: Theory of Matrix Functions; Chapter 2: Applications; Chapter 3: Conditioning; Chapter 4: Techniques for General Functions; Chapter 5: Matrix Sign Function; Chapter 6: Matrix Square Root; Chapter 7: Matrix pth Root; Chapter 8: The Polar Decomposition; Chapter 9: Schur-Parlett Algorithm; Chapter 10: Matrix Exponential; Chapter 11: Matrix Logarithm; Chapter 12: Matrix Cosine and Sine; Chapter 13: Function of Matrix Times Vector: f(A)b; Chapter 14: Miscellany; Appendix A: Notation; Appendix B: Background: Definitions and Useful Facts; Appendix C: Operation Counts; Appendix D: Matrix Function Toolbox; Appendix E: Solutions to Problems; Bibliography; Index.

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Page Count

431

Publisher

SIAM

Published Date

ISBN 10

0898716462

ISBN 13

9780898716467

King Arthur

The Making of the Legend

By: Nicholas J. Higham

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King Arthur

The Making of the Legend

By: Nicholas J. Higham

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Solve jigsaw puzzle

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Page Count

339

Publisher

Yale University Press

Published Date

ISBN 10

0300240864

ISBN 13

9780300240863

MATLAB Guide

Third Edition

By: Desmond J. Higham,Nicholas J. Higham

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MATLAB Guide

Third Edition

By: Desmond J. Higham,Nicholas J. Higham

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Solve jigsaw puzzle

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Page Count

485

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SIAM

Published Date

ISBN 10

1611974658

ISBN 13

9781611974652

Book's by Nicholas J. Higham

Functions of Matrices

Functions of Matrices

Handbook of Writing for the Mathematical Sciences

Handbook of Writing for the Mathematical Sciences

MATLAB Guide

MATLAB Guide

Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms

The Anglo-Saxon World

The Anglo-Saxon World

King Arthur

King Arthur

Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms

Functions of Matrices

Functions of Matrices

King Arthur

King Arthur

MATLAB Guide

MATLAB Guide

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