A direct method for solving linear systems by transforming the matrix into an upper triangular form and then performing back substitution. Decomposes a matrix into the product of a lower triangular ...

A fast parallel algorithm, which is generalized from the parallel algorithms for solving banded linear systems, is proposed to solve sparse triangular systems. The original problem is transformed into ...

With the increasing spread of GPUs as hardware accelerators for scientific applications, several optimized linear algebra libraries have emerged to make use of this additional computing power. In this ...

In this talk, I will present highly scalable communication-avoiding algorithms for sparse LU factorization and sparse triangular solver. The communication-avoiding "3Dimension(D)" algorithms for ...

In the case of Bidiagonal matrices, the eigenvalues can be read off the diagonal with no computation, and eigenvectors can be obtained in O(m^2) time (one linear-time solve per eigenvector). Similarly ...

Explore the fundamentals of the Finite Element Method (FEM), one of the most powerful computational tools used in engineering analysis. This introductory video breaks down the core concepts behind FEM ...