Abstract: A method and system for retrieving information in response to an information retrieval request comprises extracting additional information from a first corpus of data elements based on the request. The request is modified based on the additional information to refine the scope of information to be retrieved from a second corpus of data elements. The information is retrieved from the second corpus of data elements based on the modified request.

Abstract: A fast direct method for the solution of structured linear systems of equations. A linear system with a matrix that possesses larger submatrices that are of low ranck (to some precision).

Abstract: A machine for determining field-dependent physical characteristics contains tables of precomputed quadratures and employs them to integrate numerically over a problem boundary. The quadratures are based on products of a kernel function and a basis that spans a wide range of density functions. The kernel function is dependent on a target node's position, and different quadratures are precomputed for different target-node positions or ranges thereof. In the case of at least some of the quadratures, some the basis functions include integrable singularities. The solver divides the problem boundary into a plurality of problem intervals, to which it maps the canonical interval. To integrate a problem interval for a target point, the solver employs a precomputed quadrature that is associated with the target point's relative position and that was generated by using a basis in which a singularity occurs at each canonical-interval location that was mapped to a geometrical singularity on the problem interval.