The most critical component of any adaptive numerical quadrature routine is the estimation
of the integration error. Since the publication of the first algorithms in the 1960s, many error …

An adaptive mesh refinement method for solving optimal control problems is developed. The
method employs orthogonal collocation at Legendre–Gauss–Radau points, and adjusts …

An object-oriented MATLAB system is described that extends the capabilities of Chebfun to
smooth functions of two variables defined on rectangles. Functions are approximated to …

We present a unified and self-contained treatment of rational Krylov methods for
approximating the product of a function of a linear operator with a vector. With the help of …

The goal of this book is to teach the art of finding the root of a single algebraic equation or a
pair of such equations. We shall quote theorems and theory as necessary, but this is not …

Computing rational minimax approximations can be very challenging when there are
singularities on or near the interval of approximation---precisely the case where rational …

The Remez algorithm, 75 years old, is a famous method for computing minimax polynomial
approximations. Most implementations of this algorithm date to an era when tractable …

In Matlab, it would be good to be able to solve a linear differential equation by typing u= L\f,
where f, u, and L are representations of the right-hand side, the solution, and the differential …

We provide a new method to approximate a (possibly discontinuous) function using
Christoffel–Darboux kernels. Our knowledge about the unknown multivariate function is in …

What if all you had to do to solve an ODE were just to write it down? 1 That is the line we will
follow in this book. Our emphasis is not just on the mathematics of ODEs, but on how the …