Optimization of Triangular and Banded Matrix Operations Using 2d-Packed Layouts

Using Non-canonical Array Layouts in Dense Matrix Operations

We present two implementations of dense matrix multiplication based on two different non-canonical array layouts: one based on a hypermatrix data structure (HM) where data submatrices are stored using a recursive layout; the other based on a simple block data layout with square blocks (SB) where blocks are arranged in column-major order. We show that the iterative code using SB outperforms a re...

Investigation of Utilizing a Secant Stiffness Matrix for 2D Nonlinear Shape Optimization and Sensitivity Analysis

In this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. To approach this aim the analytical formulas of secant stiffness matrix are presented. The models were validated and used to perform inve...

Differential Polynomial Rings of Triangular Matrix Rings

Differentiation of matrix functionals using triangular factorization

In various applications, it is necessary to differentiate a matrix functional w(A(x)), where A(x) is a matrix depending on a parameter vector x. Usually, the functional itself can be readily computed from a triangular factorization of A(x). This paper develops several methods that also use the triangular factorization to efficiently evaluate the first and second derivatives of the functional. B...

synthesis of amido alkylnaphthols using nano-magnetic particles and surfactants

we used dbsa and nano-magnetic for the synthesis of amido alkylnaphtols.