The present work proposes a new method to the problem of implementation of Input-State feedback linearization. Such method is based on the search of a diffeomorphism which transforms the original nonlinear system into a linear one in the controllable canonical form with an external reference input, and the subsequent using of linear pole-placement techniques. The problem is solved without need ...

In this article, experimental situations are considered where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks, not necessarily of same size. Assuming the block sizes to be even for all blocks, for the case n ≡ 2 (mod 4), optimal designs are obtained with respect to type 1 and type 2 optimality criteria in the class of designs provi...

The Fast Fourier Transform (FFT) is based on an important factorization of the Fourier matrix Fn into a product of sparse matrices. In this paper, we demonstrate the existence of a set of FFT-like factorizations for an arbitrary Kronecker product of Fourier matrices F = Fn1 ⊗ . . . ⊗ Fnk . We show that there exists such a factorization for any chain of nested subgroups of the Abelian group Zn1×...

We study the quaternionic linear system which is composed out of terms of the form ln(x) := ∑n p=1 apxbp with quaternionic constants ap, bp and a variable number n of terms. In the first place we investigate one equation in one variable. If n = 2 the corresponding equation, which is normally called Sylvester’s equation will be treated completely by using only quaternionic algebra. For larger n ...

We study the Gaussian and robust covariance estimation, assuming the true covariance matrix to be a Kronecker product of two lower dimensional square matrices. In both settings we define the estimators as solutions to the constrained maximum likelihood programs. In the robust case, we consider Tyler’s estimator defined as the maximum likelihood estimator of a certain distribution on a sphere. W...

In kernel machines, such as kernel principal component analysis (KPCA), Gaussian Processes (GPs), and Support Vector Machines (SVMs), the computational complexity of finding a solution is O(n), where n is the number of training instances. To reduce this expensive computational complexity, we propose using Kronecker factorization, which approximates a positive definite kernel matrix by the Krone...

Some prosperities of matrix product are presented in the paper, Kronecker product, Khatri-Rao product, Hadamard product and outer product are involved. And we get some results that a multilinear tensor can be represented by the product of matrix product for a three order tensor. For higher tensor, we conjure that the same results also hold. By the representation of matrix, we give an iterative ...