Accelerating Scientific Discovery with Low Precision Floating-Point Arithmetic
A New Approach to Probabilistic
Rounding Error Analysis (Feng Kang Distinguished Lecture, 2019).
Exploiting Half Precision Arithmetic in Solving Linear Systems (Feng Kang Distinguished Lecture, 2019).
Exploiting Half Precision Arithmetic in Solving Ax = b (2019).
- Tricks and Tips in Numerical
Computing, JuliaCon 2018, London.
Multiprecision Algorithms (EMS School in Applied Mathematics
Matrix Functions and their Sensitivity (2018).
Multiprecision Algorithms (Samuel D. Conte Distinguished Lecture,
Multiprecision Algorithms (EU Regional School lectures, 2018).
Video of lectures.
Iterative Refinement in Three Precisions for Fast and Accurate Solution of
Ill-Conditioned Sparse Linear Systems (2018).
Multiprecision Algorithms (2018).
The Rise of Multiprecision Computations (2017).
See write-up on talk
by George Constantinides.
The Rise of Multiprecision Computations (2017).
of talk given at SAMSI.
Challenges in Multivalued Matrix Functions (2017).
of talk given at North Carolina State University.
Charlie Van Loan and the Matrix Exponential (2016).
Challenges in Multivalued Matrix Functions (2016).
Anderson Acceleration of the Alternating Projections Method for
Computing the Nearest Correlation Matrix, poster (2015).
Recent Progress on the Nearest Correlation Matrix Problem
Rehabilitating Invalid Correlation Matrices
How and Why to Estimate Condition Numbers for Matrix Functions
Matrix Logarithm: from Theory to Computation (2014).
and Why to Estimate Condition Numbers for Matrix Functions (2013).
Functions of Matrices
(talk at the Gene Golub SIAM Summer School 2013).
Rehabilitating Correlations, Avoiding Inversion, and
Extracting Roots (2013).
Functions of Matrices and Nearest Correlation Matrices (2013).
Numerical Issues in Testing Linear Algebra Algorithms (2013).
Bringing New Algorithms in Numerical Linear Algebra to Industry (2013).
Can You Count on Your Computer (2013).
Accuracy And Stability of Numerical Algorithms (2013).
Challenges in Exploiting Higher Precision Floating Point Arithmetic
The Matrix Logarithm: from Theory to Computation
Backward Stability of Iterations for Computing the Polar Decomposition
Functions of Matrices and
Nearest Correlation Matrices (2011).
Numerical Linear Algebra in the UK: from Cayley to Exascale
Computing (Public Lecture, 2011).
The f(A)b Problem (2011).
Functions of a Matrix: Theory, Applications and Computation (2011).
A Schur-Padé Algorithm for Fractional Powers of a Matrix (2010).
How and How Not to Compute the Exponential of a Matrix (2010).
Video of the talk given at
NAG AGM (technical session).
Computing the Action of the Matrix Exponential (2010).
Roots of Matrices (2009).
Cayley, Sylvester, and Early Matrix Theory (2009).
Computing a Nearest Correlation Matrix with Factor Structure
Video of the talk available from
(registration may be required)
Scaling, Sensitivity and Stability
in Numerical Solution of
the Quadratic Eigenvalue Problem (2009).
An Improved Arc Algorithm for Detecting Definite Hermitian
How and How Not to Compute the Exponential of a Matrix (2009).
Recent Progress in Computing the Matrix Exponential and its
Fréchet Derivative (2008).
Computing the Fréchet Derivative of the Matrix Exponential,
with an Application to Condition Number Estimation (2008).
Ralph Byers, the Matrix Sign Function, and the Polar
Useful Results in the Theory of Matrix Functions (2007).
Analysis of the Matrix Logarithm (2007).
of Matrices: From Cayley and Sylvester to MATLAB (2007). Extended
abstract of talk.
Canonical Polar Decomposition: Theory and Computation (2007).
You Count on Your Correlation Matrix? (2006). Video
of the talk available from the Wilmott site (registration required).
of a Matrix: Theory and Computation (2006)
for Matrix Roots: Convergence and Stability (2006)
f(A)b for Matrix Functions f (2006)
Matrix Functions by Iteration: Convergence, Stability and the Role of Padé Approximants (2006)
the Polynomial Eigenvalue Problem by Linearization (2006)
for Solving the Polynomial Eigenvalue Problem (2006)
Theorems in Matrix Analysis, with Applications (2006)
You ``Count'' On Your Computer (lecture for Foundation year [pre-university]
Numerical Linear Algebra in the UK , 2005.
and Stability of Iterations for Matrix Functions (2005)
Algorithms for the Matrix Cosine and Sine (2005)
Polynomial Eigenproblems by Linearization (2005) [for engineering
Conditioning of Polynomial Eigenproblem Linearizations (2005)
the Matrix Square Root in a Matrix Group (2004)
Scaling and Squaring Method for the Matrix Exponential Revisited (2004)
Functions Preserving Group Structure and Iterations for the Matrix Square
Iterations on Matrix Groups (2003)
Matrices: Properties and Generation (2003)
Functions: Theory and Algorithms (2003)
the Polar Decomposition in Matrix Groups (2003)
Results on Accuracy and Stability of Numerical Algorithms (2002)
the Indefinite Least Squares Problem by Hyperbolic QR Factorization (2002)
the Nearest Correlation Matrix - A Problem from Finance (2002). Video
of the talk , given at ERCIM Working Group on Matrix Computations and
Statistics Workshop, IRISA, Rennes, Feburary 2002.
and Stability of Numerical Algorithms (2001)
to Detect and Destroy Definiteness of Generalized and Quadratic Eigenvalue
for Polynomial Eigenvalue Problems: Theory, Computation and Applications (2001)
Pseudospectra for Polynomial Eigenvalue Problems, with Applications (2000)
the Indefinite Linear Least Squares Problem (2000)
Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm
a Quadratic Matrix Equation by Newton's Method with Exact Line Searches (1999)
Factorization with Complete Pivoting and Accurate Computation of the SVD (1998)
Nearest Definite Pair and the Inner Numerical Radius (1998)
You ``Count'' On Your Computer (public lecture for Science Week 1998)
Symmetric Indefinite Factorization: Stability and Applications in Optimization (1997)
and How Not to Compute the Matrix Square Root (1997)
of Householder QR Factorization for Weighted Least Squares Problems (1997)
d'Erreur Inverse Pour le Probleme des Moindres Carres (in French)
the Inertias of Matrices Arising in Optimization (1996)
Pure, Applied, and for Fun (1996)
the Field of Values and Pseudospectra Using the Lanczos Method with Continuation (1996)
Linear Algebra Software (1996)
Wilkinson, and Gaussian Elimination (1996)
Errors in Eigenvalue Computations (1995)
in Floating Point Computation---And How to Avoid Them (1995)
and How Not to Sum Floating Point Numbers (1995)
Results on the Accuracy and Stability of Least Squares Solvers (1994)
Procrustes Problems (1994)