C++ implementations of numerical methods for solving differential-algebraic equations: design and optimization considerations
Object-oriented programming can produce improved implementations of complex numerical methods, but it can also introduce a performance penalty. Since computational simulation often requires intricate and highly efficient codes, the performance penalty of ...
A frontal code for the solution of sparse positive-definite symmetric systems arising from finite-element applications
We describe the design, implementation, and performance of a frontal code for the solution of large sparse symmetric systems of linear finite-element equations. The code is intended primarily for positive-definite systems, since numerical pivoting is not ...
Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form
A two-stage blocked algorithm for reduction of a regular matrix pair (A , B ) to upper Hessenberg-triangular form is presented. In stage 1 (A, B is reduced to block upper Hessenberg-triangular form using mainly level 3 (matrix-matrix) operations that ...
Characteristic spectra of the curvature functional: a numerical study in bifurcation
A method is described for the eignevalues of piecewise smooth C2 extremum-energy curves. Typical interpolants are investigated within the framework of their eigensystems, and conclusions are presented concerning their natural modes of vibration, ...