in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.

We give a simple proof that an n×n orthogonal matrix with n ≥ 2 which cannot be written as a direct sum has at least 4n− 4 nonzero entries. 1. The result. What is the least number of nonzero entries in a real orthogonal matrix of order n? Since the identity matrix In is orthogonal the answer is clearly n. A more interesting question is: what is the least number of nonzero entries in a real orth...

Block Wavelet Transforms (BWTs) are orthogonal matrix transforms that can be obtained from orthogonal subband filter banks. They were initially generated to produce matrix transforms which may carry nice properties inheriting from wavelets, as alternatives to DCT and similar matrix transforms. Although the construction methodology of BWT is clear, the reverse operation was not researched. In ce...

In this paper, we examine stability issues that arise when computing the search directions (Ax, Ay, As) for a primal-dual path-following interior point method for linear programming. The dual step Ay can be obtained by solving a weighted least-squares problem for which the weight matrix becomes extremely ill conditioned near the boundary of the feasible region. Hough and Vavasis proposed using ...

Orthogonal matrix has shown advantages in training Recurrent Neural Networks (RNNs), but such matrix is limited to be square for the hidden-to-hidden transformation in RNNs. In this paper, we generalize such square orthogonal matrix to orthogonal rectangular matrix and formulating this problem in feedforward Neural Networks (FNNs) as Optimization over Multiple Dependent Stiefel Manifolds (OMDSM...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...