A fundamental computational procedure in practically all areas of scientific computing is the calculation of the Newton step (in n-dimensions). In many cases this computation represents the dominant cost in the overall computing task. Typically the Newton step computation breaks down into two separable subtasks: calculation of the Jacobian (or Hessian) matrix along with the right-hand-side, and...

In particular, the distance from a point x ∈ R to a hyperplane H where x / ∈ H , is given by the length of the perpendicular line segment from x to H . If two hyperplanes H1, H2 are parallel, their normal vectors are multiples of each other, so we can take a single normal vector u and write H1 = {x : (x, u) = α1} and H2 = {x : (x, u) = α2}. Take any x ∈ H1 . Then d(x,H2) is given by the perpend...

The author came to lateral line research rather by chance, yet this sensory system ended up as the main focus of my entire scientific career. This paper is not a review article. Instead, it gives an overview some major topics that author, collaborators, and students have worked on for more than 4 decades. During last century, was mostly approached using mono-frequency water motions generated in...