We study Dickson bases for binary field representation. Such representation seems interesting when no optimal normal basis exists for the field. We express the product of two elements as Toeplitz or Hankel matrix vector product. This provides a parallel multiplier which is subquadratic in space and logarithmic in time.

When a square matrix A, is diagonalizable, (for example, when A is Hermitian or has distinct eigenvalues), then An can be written as a sum of the nth powers of its eigenvalues with matrix weights. However, if a 1 occurs in its Jordan form, then the form is more complicated: An can be written as a sum of polynomials of degree n in its eigenvalues with coefficients depending on n. In this case to...

We investigate a new representation of general operators by means of sums of shifted Gabor multipliers. These representations arise by studying the matrix of an operator with respect to a Gabor frame. Each shifted Gabor multiplier corresponds to a side-diagonal of this matrix. This representation is especially useful for operators whose associated matrix possesses some offdiagonal decay. In thi...

A noncoherent optical vector-matrix multiplier using a linear LED source array and a linear P-I-N photodiode detector array has been combined with a 1-D adder in a feedback loop. The resultant iterative optical processor and its use in solving simultaneous linear equations are described. Operation on complex data is provided by a novel color-multiplexing system.

The Variational Iteration Method (VIM) is an iterative method that approximates solutions of differential equations. The method is a modification of the so-called general Lagrange multipliers [2]. The method is based on the idea of constructing a correction functional that uses a Lagrange multiplier. In this study, we analyse some basic properties of the Lagrange multiplier; and using these, we...

Attitude quaternion [1] is the attitude parameterization of choice for spacecraft attitude estimation for several reasons: 1) it is free of singularities, 2) the attitude matrix is quadratic in the quaternion components, and 3) the kinematics equations is bilinear and an analytic solution exists for the propagation. However, the components of the attitude quaternion are not independent of each ...