SIAM Review

The first Survey and Review article in this issue is “Symplectic Runge--Kutta Schemes for Adjoint Equations, Automatic Differentiation, Optimal Control, and More,” by J. M. Sanz-Serna. It looks at an aspect of geometric integration, a term first coined by ...

The study of the sensitivity of the solution of a system of differential equations with respect to changes in the initial conditions leads to the introduction of an adjoint system, whose discretization is related to reverse accumulation in automatic ...

In physics, it is sometimes desirable to compute the so-called density of states (DOS), also known as the spectral density, of a real symmetric matrix $A$. The spectral density can be viewed as a probability density distribution that measures ...

The Research Spotlights section contains two papers in this issue. First, “Geodesic Transport Barriers in Jupiter's Atmosphere: A Video-Based Analysis," by Alireza Hadjighasem and George Haller, describes a dynamical analysis of the Great Red Spot of ...

Jupiter's zonal jets and Great Red Spot are well known from still images. However, the planet's atmosphere is highly unsteady, which suggests that the actual material transport barriers delineating its main features should be time-dependent. Rare video ...

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the union of a negative ...

The SIGEST paper in this issue, “A Newton--Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics,” by M. Schick, V. Heuveline, and O. P. Le Ma\^\itre, is from the SIAM-ASA Journal on Uncertainty Quantification (JUQ). JUQ is a new journal, and ...

The determination of limit-cycles plays an important role in characterizing complex dynamical systems, such as unsteady fluid flows. In practice, dynamical systems are described by models equations involving parameters which are seldom exactly known, ...

The rigorous understanding of games has a long history in the mathematical sciences, attracting the interest of greats like Borel, von Neumann, and Shannon. Great games like chess and go admit so many variations (Shannon estimated $10^{120}$ possible game ...

We analyze the traditional board game the Game of the Goose. We are particularly interested in the probabilities of the different players winning, and we show that we can determine these probabilities exactly for up to six players and using simulation for ...

Six months ago I sent out an appeal, especially to young people in the field, asking them to let me know if they are interested in writing book reviews for SIAM. I've received several responses, for which I am grateful. In most of these cases I have not ...