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...

A new method is described for computing the singular value decomposition (SVD). It begins by computing the polar decomposition and then computes the spectral decomposition of the Hermitian polar factor. The method is particularly attractive for shared memory parallel computers with a relatively small number of processors, because the polar decomposition can be computed efficiently on such machi...

A new method is described for computing the singular value decomposition (SVD). It begins by computing the polar decomposition and then computes the spectral decomposition of the Hermitian polar factor. The method is particularly attractive for shared memory parallel computers with a relatively small number of processors, because the polar decomposition can be computed efficiently on such machi...

Modern bytecode execution environments with optimizing just-in-time compilers, such as Sun’s Hotspot Java Virtual Machine, IBM’s Java Virtual Machine, and Microsoft’s Common Language Runtime, provide an infrastructure for generating fast code at runtime. Such runtime code generation can be used for efficient implementation of parametrized algorithms. More generally, with runtime code generation...

A previously introduced two phase model was used to assess its capability in predicting the behavior of reinforced soil walls under working stress conditions. The two phase model is a homogenization method based on the virtual work theorem. The reinforced soil medium is considered as the superposition of two continuous phases, the reinforcement and matrix phases that interact within the medium....

The solution of the Hartree-Fock equations involves the iterative construction of the Fock matrix based on approximate molecular orbit& and the diagonal&&ion of that Fock matrix to obtain new approximations to those orbitals. A significant portion of this work is unnecessary, however, because the occupied molecular orbitals, which are required to construct the Fock matrix, represent a small fra...

In order to reveal quantitative trait loci (QTL) interactions and the relationship between various interactions in complex traits, we have developed a new QTL mapping approach, named genotype matrix mapping (GMM), which searches for QTL interactions in genetic variation. The central approach in GMM is the following. (1) Each tested marker is given a virtual matrix, named a genotype matrix (GM),...