Higham, Nicholas J. 1961
Overview
Works:  85 works in 357 publications in 2 languages and 4,020 library holdings 

Genres:  Guidebooks 
Roles:  Author, Editor, Contributor, Opponent, 958 
Classifications:  QA297, 808.06651 
Publication Timeline
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Most widely held works by
Nicholas J Higham
Handbook of writing for the mathematical sciences by
Nicholas J Higham(
Book
)
53 editions published between 1993 and 2010 in English and Japanese and held by 983 WorldCat member libraries worldwide
General literature  Reference
53 editions published between 1993 and 2010 in English and Japanese and held by 983 WorldCat member libraries worldwide
General literature  Reference
MATLAB guide by
Desmond J Higham(
Book
)
52 editions published between 2000 and 2017 in English and held by 842 WorldCat member libraries worldwide
"This second edition of MATLAB Guide completely revises and updates the first edition and is more than 30% longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox."BOOK JACKET
52 editions published between 2000 and 2017 in English and held by 842 WorldCat member libraries worldwide
"This second edition of MATLAB Guide completely revises and updates the first edition and is more than 30% longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox."BOOK JACKET
Accuracy and stability of numerical algorithms by
Nicholas J Higham(
Book
)
38 editions published between 1996 and 2002 in English and held by 713 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
38 editions published between 1996 and 2002 in English and held by 713 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
The Princeton companion to applied mathematics by
Nicholas J Higham(
Book
)
15 editions published between 2015 and 2017 in English and held by 364 WorldCat member libraries worldwide
This is the most authoritative and accessible singlevolume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important questions, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a userfriendly reference book on applied mathematics.  Front jacket flap
15 editions published between 2015 and 2017 in English and held by 364 WorldCat member libraries worldwide
This is the most authoritative and accessible singlevolume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important questions, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a userfriendly reference book on applied mathematics.  Front jacket flap
Functions of matrices : theory and computation by
Nicholas J Higham(
Book
)
19 editions published in 2008 in English and held by 346 WorldCat member libraries worldwide
"Functions of Matrices: Theory and Computation gives a thorough treatment of the theory of matrix functions and numerical methods for computing them, as well as an overview of applications. The book is useful for advanced courses and is wellsuited to selfstudy. The broad content  including f(A)related facts, tricks, and techniques, historical references, and an appendix of background results  makes it convenient as a general reference in matrix analysis and numerical linear algebra."Jacket
19 editions published in 2008 in English and held by 346 WorldCat member libraries worldwide
"Functions of Matrices: Theory and Computation gives a thorough treatment of the theory of matrix functions and numerical methods for computing them, as well as an overview of applications. The book is useful for advanced courses and is wellsuited to selfstudy. The broad content  including f(A)related facts, tricks, and techniques, historical references, and an appendix of background results  makes it convenient as a general reference in matrix analysis and numerical linear algebra."Jacket
Fast polar decomposition of an arbitrary matrix by
Nicholas J Higham(
Book
)
2 editions published in 1988 in English and held by 72 WorldCat member libraries worldwide
"The polar decomposition of an m x n matrix A of full rank, where m [greater than or equal to] n, can be computed using a quadratically convergent algorithm of Higham. The algorithm is based on a Newton iteration involving a matrix inverse. We show how with the use of a preliminary complete orthogonal decomposition the algorithm can be extended to arbitrary A. We also describe how to use the algorithm to compute the positive semidefinite square root of a Hermitian positive semidefinite matrix
2 editions published in 1988 in English and held by 72 WorldCat member libraries worldwide
"The polar decomposition of an m x n matrix A of full rank, where m [greater than or equal to] n, can be computed using a quadratically convergent algorithm of Higham. The algorithm is based on a Newton iteration involving a matrix inverse. We show how with the use of a preliminary complete orthogonal decomposition the algorithm can be extended to arbitrary A. We also describe how to use the algorithm to compute the positive semidefinite square root of a Hermitian positive semidefinite matrix
Improved error bounds for underdetermined system solvers by
James W Demmel(
Book
)
9 editions published in 1990 in English and held by 14 WorldCat member libraries worldwide
We show that these error bounds can be strengthened by replacing [subscript K₂](A) by the potentially much smaller quantity cond₂(A) = [formula], which is invariant under row scaling of A. We also show that cond₂(A) reflects the sensitivity of the minimum norm solution x to row wise relative perturbations in the data A and b. For square linear system Ax = b row equilibration is shown to endow solution methods based on LU or QR factorization of A with relative error bounds proportional to cond[subscript [infinity]](A), just as when a QR factorization of A[superscript T] is used. The advantages of using fixed precision iterative refinement in this context instead of row equilibration are explained."
9 editions published in 1990 in English and held by 14 WorldCat member libraries worldwide
We show that these error bounds can be strengthened by replacing [subscript K₂](A) by the potentially much smaller quantity cond₂(A) = [formula], which is invariant under row scaling of A. We also show that cond₂(A) reflects the sensitivity of the minimum norm solution x to row wise relative perturbations in the data A and b. For square linear system Ax = b row equilibration is shown to endow solution methods based on LU or QR factorization of A with relative error bounds proportional to cond[subscript [infinity]](A), just as when a QR factorization of A[superscript T] is used. The advantages of using fixed precision iterative refinement in this context instead of row equilibration are explained."
Stability of block algorithms with fast level 3 BLAS by
James W Demmel(
Book
)
7 editions published between 1990 and 1991 in English and held by 10 WorldCat member libraries worldwide
A second implication is that the use of BLAS3 based on fast matrix multiplication techniques affects the stability only insofar as it increases the constant terms in the normwise backward error bounds. For linear equation solvers employing LU factorization it is shown that fixed precision iterative refinement helps to mitigate the effect of the larger error constants. The analysis is illustrated with the aid of numerical examples."
7 editions published between 1990 and 1991 in English and held by 10 WorldCat member libraries worldwide
A second implication is that the use of BLAS3 based on fast matrix multiplication techniques affects the stability only insofar as it increases the constant terms in the normwise backward error bounds. For linear equation solvers employing LU factorization it is shown that fixed precision iterative refinement helps to mitigate the effect of the larger error constants. The analysis is illustrated with the aid of numerical examples."
A collection of test matrices in MATLAB by
Nicholas J Higham(
Book
)
6 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
Abstract: "We present a collection of fortyfour parameterized test matrices. The matrices are mostly square, dense, nonrandom, and of arbitrary dimension. The collection includes matrices with known inverses or known eigenvalues; illconditioned or rank deficient matrices; and symmetric, positive definite, orthogonal, defective, involuntary, and totally positive matrices. For each matrix we give a MATLAB Mfile that generates it, and, for small dimensions, a printout of the matrix, pictures of it, and a plot of its field of values."
6 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
Abstract: "We present a collection of fortyfour parameterized test matrices. The matrices are mostly square, dense, nonrandom, and of arbitrary dimension. The collection includes matrices with known inverses or known eigenvalues; illconditioned or rank deficient matrices; and symmetric, positive definite, orthogonal, defective, involuntary, and totally positive matrices. For each matrix we give a MATLAB Mfile that generates it, and, for small dimensions, a printout of the matrix, pictures of it, and a plot of its field of values."
Block LU factorization by
James W Demmel(
Book
)
6 editions published in 1992 in English and held by 8 WorldCat member libraries worldwide
6 editions published in 1992 in English and held by 8 WorldCat member libraries worldwide
How accurate is Gaussian elimination? by
Nicholas J Higham(
Book
)
6 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
Particular topics include: classes of matrix for which it is advantageous not to pivot; how to estimate or compute the backward error; iterative refinement in single precision; and how to compute efficiently a bound on the forward error."
6 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
Particular topics include: classes of matrix for which it is advantageous not to pivot; how to estimate or compute the backward error; iterative refinement in single precision; and how to compute efficiently a bound on the forward error."
Proceedings of the Eighth Conference of the International Linear Algebra Society : (19  22 July 1999, Barcelona, Spain) by
International Linear Algebra Society(
Book
)
4 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
4 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
The Test Matrix Toolbox for MATLAB by
Nicholas J Higham(
Book
)
3 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Perturbation theory and backward error for AXXB=C by
Nicholas J Higham(
Book
)
4 editions published in 1992 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 1992 in English and held by 6 WorldCat member libraries worldwide
Parallel singular value decomposition via the polar decomposition by
Nicholas J Higham(
Book
)
3 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Stability of the partitioned inverse method for parallel solution sparse triangular systems by
Nicholas J Higham(
Book
)
4 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
4 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Bounding the error in Gaussian elimination for tridiagonal systems by
Nicholas J Higham(
Book
)
3 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
"If x̂ is the computed solution to a tridiagonal system Ax = b obtained by Gaussian elimination, what is the "best" bound available for the error x  x̂ and how can it be computed efficiently? This question is answered using backward error analysis, perturbation theory, and properties of the LU factorization of A. For three practically important classes of the tridiagonal matrix, those that are symmetric positive definite, totally nonnegative, or are Mmatrices, it is shown that (A+E)x̂ = b where the backward error matrix E is small componentwise relative to A. For these classes of matrix the appropriate forward error bound involves Skeel's condition number cond(A, x), which we show can be computed exactly in O(n) operations. For diagonally dominant tridiagonal A the same type of backward error result holds and we obtain a useful upper bound for cond(A, x) which can be computed in O(n) operations. We also discuss error bounds and their computation for general tridiagonal matrices."
3 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
"If x̂ is the computed solution to a tridiagonal system Ax = b obtained by Gaussian elimination, what is the "best" bound available for the error x  x̂ and how can it be computed efficiently? This question is answered using backward error analysis, perturbation theory, and properties of the LU factorization of A. For three practically important classes of the tridiagonal matrix, those that are symmetric positive definite, totally nonnegative, or are Mmatrices, it is shown that (A+E)x̂ = b where the backward error matrix E is small componentwise relative to A. For these classes of matrix the appropriate forward error bound involves Skeel's condition number cond(A, x), which we show can be computed exactly in O(n) operations. For diagonally dominant tridiagonal A the same type of backward error result holds and we obtain a useful upper bound for cond(A, x) which can be computed in O(n) operations. We also discuss error bounds and their computation for general tridiagonal matrices."
Stability of parallel triangular system solvers by
Nicholas J Higham(
Book
)
2 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
Exploiting fast matrix multiplication within the level 3 BLAS by
Nicholas J Higham(
Book
)
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
Abstract: "The level 3 BLAS (BLAS3) are a set of specifications of Fortran 77 subprograms for carrying out matrix multiplications and the solution of triangular systems with multiple righthand sides. They are intended to provide efficient and portable building blocks for linear algebra algorithms on high performance computers. We describe algorithms for the BLAS3 operations that are asymptotically faster than the conventional ones. These algorithms are based on Strassen's method for fast matrix multiplication, which is now recognized to be a practically useful technique once matrix dimensions exceed about 100. We pay particular attention to the numerical stability of these "fast BLAS3". Error bounds are given and their significance is explained and illustrated with the aid of numerical experiments. Our conclusion is that the fast BLAS3, although not as strongly stable as conventional implementations, are stable enough to be suitable for many applications."
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
Abstract: "The level 3 BLAS (BLAS3) are a set of specifications of Fortran 77 subprograms for carrying out matrix multiplications and the solution of triangular systems with multiple righthand sides. They are intended to provide efficient and portable building blocks for linear algebra algorithms on high performance computers. We describe algorithms for the BLAS3 operations that are asymptotically faster than the conventional ones. These algorithms are based on Strassen's method for fast matrix multiplication, which is now recognized to be a practically useful technique once matrix dimensions exceed about 100. We pay particular attention to the numerical stability of these "fast BLAS3". Error bounds are given and their significance is explained and illustrated with the aid of numerical experiments. Our conclusion is that the fast BLAS3, although not as strongly stable as conventional implementations, are stable enough to be suitable for many applications."
Matrix powers in finite precision arithmetic by
Nicholas J Higham(
Book
)
2 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
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Related Identities
 Higham, Desmond J. 1964 Author
 Dennis, Mark R. Editor
 Society for Industrial and Applied Mathematics
 Schreiber, Robert S.
 Research Institute for Advanced Computer Science (U.S.)
 University of Manchester Department of Mathematics
 Demmel, James Author
 Manchester Centre for Computational Mathematics
 Knight, P. A.
 Victoria University Department of Mathematics
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Associated Subjects
Adaptive signal processing Algebra Algebras, Linear Algorithms Computational complexity Computer algorithms Computer programs Computer software Error analysis (Mathematics) Factorization (Mathematics) Functions Gaussian processes Information theory Mathematical models Mathematical statistics Mathematics MathematicsAuthorship MATLAB Matrices Multiprocessors Numerical analysis Numerical analysisComputer programs Numerical analysisData processing Operations research Signal processing System analysis Technical writing