  The current computer architecture has moved towards the multi/many-core
structure. However, the algorithms in the current sequential dense numerical
linear algebra libraries (e.g. LAPACK) do not parallelize well on
multi/many-core architectures. A new family of algorithms, the tile algorithms,
has recently been introduced to circumvent this problem. Previous research has
shown that it is possible to write efficient and scalable tile algorithms for
performing a Cholesky factorization, a (pseudo) LU factorization, and a QR
factorization. The goal of this thesis is to study tiled algorithms in a
multi/many-core setting and to provide new algorithms which exploit the current
architecture to improve performance relative to current state-of-the-art
libraries while maintaining the stability and robustness of these libraries.
