Given a complex matrix H, we consider the decomposition H = QRP∗, where R is upper triangular and Q and P have orthonormal columns. Special instances of this decomposition include the singular value decomposition (SVD) and the Schur decomposition where R is an upper triangular matrix with the eigenvalues of H on the diagonal. We show that any diagonal for R can be achieved that satisfies Weyl’s...

this paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (tfs) in combination with the collocation method. the method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. finally, the error analysis and some numerical examples are provided...

The critical path problem is a classical and important network optimization problem appearing in many applications, especially in planning and controlling the complex projects. However the result of classical critical path method computation cannot properly match the real-world problem. This gives rise to fuzzy environment and hence we have fuzzy critical path method. In this paper, two differe...

The Extended Euclidean algorithm for matrix Pade approximants is applied to compute matrix Pade approximants in rectangular full packed format (RFP) if the coefficient matrices of the input matrix polynomial are triangular. The procedure given by Gustavson et al for packing a triangular matrix in rectangular full packed format is applied to pack sequence of lower triangular matrices of a matrix...

S U M M A R Y A Triangular Spectral Element Method (TSEM) is presented to simulate elastic wave propagation using an unstructured triangulation of the physical domain. TSEM makes use of a variational formulation of elastodynamics based on unstructured straight-sided triangles that allow enhanced flexibility when dealing with complex geometries and velocity structures. The displacement field is ...

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...

Most computer contour mapping of irregularly spaced data points is performed using an intermediate rectangular grid. An alternative method is proposed whereby a map area is automatically divided into suitable triangular domains with a data point at each vertex. Surface estimation and contour plotting are then performed independently for each triangle using a measured or bestfit plane associated...

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fu...

In this paper we develop a novel image processing technique to register two dimensional temporal mammograms for effective diagnosis and therapy. Our registration framework is founded upon triangular B-spline finite element method (TBFEM). In contrast to tensor-product B-splines, which is widely used in medical imaging, triangular B-splines are much more powerful, associated with many desirable ...