Much of this section was copied and paraphrased from Heath’s Scientific Computing. Anyways. Suppose we are looking for an orthogonal transformation that annihilates desired components of a given vector. Recall that a square real matrix Q is said to be orthogonal if its columns are orthonormal, that is, that Q Q = I. Orthogonal transformations are nice because they preserve Euclidean norms of an...

In this paper, a Schwarz-Christoffel method for generating two-dimensional grids for a variety of complex internal and external flow configurations based on the numerical integration procedure of the Schwarz-Christoffel transformation has been developed by using Mathematica, which is a general purpose symbolic-numerical-graphical mathematics software. This method is highly accurate (fifth order...

In this paper, a Schwarz-Christoffel method for generating two-dimensional grids for a variety of complex internal and external flow configurations based on the numerical integration procedure of the Schwarz-Christoffel transformation has been developed by using Mathematica, which is a general purpose symbolic-numerical-graphical mathematics software. This method is highly accurate (fifth order...

A method is developed for solving the two dimensional Helmholtz equation in a duct with varying cross-section region bounded by a curved top and flat bottom, having one region inside. To compute the propagation of sound waves in a curved duct with a curved internal interface is difficult problem. One method is to transform the wave equation into a solvable form and making the curved interface p...

Consideration was given to the linearization of logical functions defined by a set of pairwise orthogonal terms. The linearization is carried out by computing the autocorrelation functions. Proposed was a method consisting of (i) calculation of the autocorrelation function in the space of orthogonal terms, (ii) generation of the corresponding matrix of linear transformation, and (iii) the linea...

Subject of the present paper is the study and construction of complete independent invariants and canonical forms for linear multivariable systems under the action of orthogonal transformation groups. Stable computational algorithms for finding the orthogonal canonical forms are presented and their numerical properties are discussed. In view of their nice numerical properties the orthogonal can...