LAPACK and LINPACK both solve symmetric inde nite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman (1977). No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small. We show that this argument is f...

LAPACK and LINPACK both solve symmetric indeenite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman (1977). No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small. We show that this argument is f...

LAPACK and LINPACK both solve symmetric indeenite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman (1977). No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small. We show that this argument is f...

LAPACK and LINPACK both solve symmetric indefinite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman [Math. Comp., 31 (1977), pp. 163–179]. No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small....

Maximal planar graphs embed in the euclidean plane as plane triangulations. Two such plane triangulations are equivalent if there is a homeomorphism of the plane which maps the vertices, edges and faces of one onto the corresponding elements of the other. A diagonal operation on a plane triangulation deletes an appropriate edge and inserts a related edge. We prove constructively that, given any...

We formulate and prove two Rice-like theorems that characterize limitations on nameability of properties within a given naming scheme for partial functions. Such a naming scheme can, but need not be, an executable formalism. A programming language is an example of an executable naming scheme, where the program text names the partial function it implements. Halting is an example of a property th...

In a multi-study naturalistic quasi-experiment involving 269 students in a semester-long introductory philosophy course, we investigated the effect of teaching argument diagramming (AD) on students’ scores on argument analysis tasks. An argument diagram is a visual representation of the content and structure of an argument. In each study, all of the students completed preand posttests containin...

In this paper a non-diagonal regulator, based on the QFT method, is synthesized for an uncertain MIMO plant whose output and control signals are subjected to hard time-domain constraints. This procedure includes the design of a non-diagonal pre-controller based on a new simple approach, followed by the sequential design of a diagonal QFT controller. We present a new formulation for the latter s...

In order to present this result, we approach it by proving some preliminary theorems about different forcings which capture the main ideas in a simpler setting. For the entirety of the notes we work with an increasing sequence of large cardinals 〈κn | n < ω〉 with κ =def supn<ω κn. The large cardinal hypothesis that we use varies with the forcing. A recurring theme is the idea of a cell. A cell ...