A Linear Algebraic View of Loop

A Linear Algebraic View of Loop Transformations and Their Interaction

Although optimizing transformations have been studied for over two decades, the interactions between them is not well understood. This is particularly important for the success of parallelizing compilers. In order to deal with interactions, we view loop transformations as multiplication by a suitable matrix. The transformations considered are loop interchange, permutation, reversal, hyperplane ...

Robust H_∞ Controller design based on Generalized Dynamic Observer for Uncertain Singular system with Disturbance

This paper presents a robust ∞_H controller design, based on a generalized dynamic observer for uncertain singular systems in the presence of disturbance. The controller guarantees that the closed loop system be admissible. The main advantage of this method is that the uncertainty can be found in the system, the input and the output matrices. Also the generalized dynamic observer is used to est...

On One-Sided Ideals of Rings of Linear Transformations

Function call overhead benchmarks with MATLAB, Octave, Python, Cython and C

where Ω ⊆ Rd is a d-dimensional domain with boundary ∂Ω and a, c, f : Ω → R, b : Ω→ Rd and g : ∂Ω→ R are given functions with special properties that will not be discussed here. In FEM a domain is discretized into a mesh by splitting the domain into “simple” geometric shapes (intervals, triangles, tetrahedrons, . . . ). Along with special functions (usually piecewise polynomials) these shapes a...

Algebraic Solving of Complex Interval Linear Systems by Limiting ‎Factors‎

In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...