Methods, apparatus, systems and articles of manufacture are disclosed to optimize sparse matrix execution. An example disclosed apparatus includes a context former to identify a matrix function call from a matrix function library, the matrix function call associated with a sparse matrix, a pattern matcher to identify an operational pattern associated with the matrix function call, and a code generator to associate a function data structure with the matrix function call exhibiting the operational pattern, the function data structure stored external to the matrix function library, and facilitate a runtime link between the function data structure and the matrix function call.