Operations with tensors, or multiway arrays, have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-1 outer products using eitherâ€¦ (More)

Abstract. Traditionally, extending the Singular Value Decomposition (SVD) to third-order tensors (multiway arrays) has involved a representation using the outer product of vectors. These outerâ€¦ (More)

Abstract. A fast method for solving a linear system of the form (A(p) âŠ— Â· Â· Â· âŠ— A(1) âˆ’ Î»I)x = b is given where each A(i) is an ni-by-ni matrix. The first step is to convert the problem to triangularâ€¦ (More)

Abstract. Suppose A = (aijk) âˆˆ RnÃ—nÃ—n is a three-way array or third-order tensor. Many of the powerful tools of linear algebra such as the singular value decomposition (SVD) do not, unfortunately,â€¦ (More)

If the complex Schur decomposition is used to solve a real linear system, then the computed solution generally has a complex component because of roundoff error. We show that the real part of theâ€¦ (More)

This paper deals with the use of interactive computer simulation and animation environments in a virtual lab which illustrates real-world applications of fundamental control principles. The goals ofâ€¦ (More)

A novel approach to the implementation of interactive virtual-labs is proposed. The model and the view of the virtual-lab are described in Modelica language, and the virtual-lab is ran using Dymola.â€¦ (More)

Systems of the form (R(1) Â· Â· Â·R(p) âˆ’ Î»I)x = b, where each R(i) is an n-by-n upper triangular matrix, can be solved in O(pn3) flops if the matrix of coefficients is explicitly formed. We develop aâ€¦ (More)