Higham, Nicholas J. 1961Overview
Publication Timeline
Most widely held works by
Nicholas J Higham
Handbook of writing for the mathematical sciences
by Nicholas J Higham
(
Book
)
39 editions published between 1993 and 2010 in English and held by 962 WorldCat member libraries worldwide This handy volume, enlivened by anecdotes, unusual paper titles, and humorous quotations, provides even more information on the issues you will face when writing a technical paper or talk, from choosing the right journal in which to publish to handling your references. Its overview of the entire publication process is invaluable for anyone hoping to publish in a technical journal
MATLAB guide
by D. J Higham
(
Book
)
33 editions published between 2000 and 2008 in English and held by 808 WorldCat member libraries worldwide 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 easytouse editing and debugging tools. This second edition of MATLAB Guide completely revises and updates the bestselling 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
Accuracy and stability of numerical algorithms
by Nicholas J Higham
(
Book
)
30 editions published between 1996 and 2002 in English and held by 713 WorldCat member libraries worldwide Accuracy and Stability of Numerical Algorithms gives a thorough, uptodate 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 skewsymmetric 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 multiplyadd operation found on some modern computer architectures
Functions of matrices : theory and computation
by Nicholas J Higham
(
Book
)
15 editions published in 2008 in English and held by 360 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."BOOK JACKET
Fast polar decomposition of an arbitrary matrix
by Nicholas J Higham
(
Book
)
2 editions published in 1988 in English and held by 63 WorldCat member libraries worldwide We formulate a hybrid algorithm which adaptively switches from the matrix inversion based iteration to a matrix multiplication based iteration due to Kovarik, and to Björck and Bowie. The decision when to switch is made using a condition estimator. This "matrix multiplication rich" algorithm is shown to be more efficient on machines for which matrix multiplication can be executed 1.5 times faster than matrix inversion."
Improved error bounds for underdetermined system solvers
by James Demmel
(
Book
)
4 editions published in 1990 in English and held by 10 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 Demmel
(
Book
)
6 editions published between 1990 and 1991 in English and held by 9 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."
Proceedings of the Eighth Conference of the International Linear Algebra Society : (19  22 July 1999, Barcelona, Spain)
by International Linear Algebra Society
(
Book
)
3 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
Accuracy and stability of numerical algorithms
by Nicholas J Higham
(
)
1 edition published in 2002 in English and held by 6 WorldCat member libraries worldwide
Handbook of writing for the mathematical sciences
by Nicholas J Higham
(
)
1 edition published in 1998 in English and held by 6 WorldCat member libraries worldwide
A collection of test matrices in MATLAB
by Nicholas J Higham
(
Book
)
3 editions published in 1989 in English and held by 5 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."
How accurate is Gaussian elimination?
by Nicholas J Higham
(
Book
)
3 editions published in 1989 in English and held by 5 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."
The Test Matrix Toolbox for MATLAB
by Nicholas J Higham
(
Book
)
2 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
Block LU factorization
by James W Demmel
(
Book
)
3 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Stability of the partitioned inverse method for parallel solution sparse triangular systems
by Nicholas J Higham
(
Book
)
3 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Bounding the error in Gaussian elimination for tridiagonal systems
by Nicholas J Higham
(
Book
)
2 editions published in 1988 in English and held by 4 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."
Exploiting fast matrix multiplication within the level 3 BLAS
by Nicholas J Higham
(
Book
)
2 editions published in 1989 in English and held by 4 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."
The matrix sign decomposition and its relation to the polar decomposition
by Nicholas J Higham
(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
A parallel algorithm for computing the polar decomposition
by Nicholas J Higham
(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Matrix powers in finite precision arithmetic
by Nicholas J Higham
(
Book
)
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide more
fewer
Audience Level
Related Identities
Associated Subjects
Adaptive signal processing Algebras, Linear Algorithms Computational complexity Computer algorithms Computer software Error analysis (Mathematics) Factorization (Mathematics) Functions Gaussian processes Mathematical statistics Mathematics MathematicsAuthorship MATLAB Matrices Numerical analysisData processing Operations research System analysis Technical writing

Alternative Names
Higham, N. J. 1961
Higham, Nicholas J
Languages
Covers
