Up To Date: large-scale linear problems require the best available algorithmic methods. This is because these problems are computationally demanding. Thus, have the best available algorithmic method can often decides the difference as to whether solving the problem is feasible or not. We pride ourselves on implementing the best innovative algorithms available. The algorithms we have work equally well on well posed and ill-posed problems.
Uniform Accuracy and Reliability: In addition, these algorithms treat symmetric and nonsymmetric equations in the same manner. This eliminates any concern users may have about the appropriateness of the algorithms being employed and the consequent impact on the reliability and accuracy of the results. Thus, users are assured of uniform quality. This quality is the same for both nonsymmetric and symmetric matrices. Users are assured that the same high-quality and accuracy is guaranteed and consistent. It is expected that the higher level of reliability and accuracy will attract more users whether they are experienced or inexperienced.
Predetermined Application Costs: finally, users know in advance the computational costs of the problem that is to be solved. This budgetary information enables users to make wise decisions far in advance before any computational effort is started. Essentially, users are able to determine the costs of engineering and physical modeling. This truly enables research firms to meet budgetary constraints.
At this time, the algorithmic literature is in a state of flux. This is especially true in the case where one is solving a nonsymmetric system of equations. There are a variety of methods available for the nonsymmetric case. Furthermore, it is not clear that one approach is clearly superior to another. And even though the conjugate method algorithm especially when it is combined with a preconditioner is widely accepted to be superior to other approaches, even this conclusion could be changing.