Partitioning Technique for Determinantal Equations
The partitioning of large arrays into block components which could themselves be manipulated as algebraic entities is a technique which has been used with particular effectiveness by P.-O. Löwdin and his school. This “partitioning technique” underlies the Löwdin analysis /1/ of the relationship between perturbation and variational treatments of Schrödinger’s equation, and leads to the resolvent algebra, inner projections, and other important formal developments. In this brief note we describe how this technique can also simplify the treatment of determinantal equations, which permit a unified approach to certain problems of numerical approximation, interpolation, and quadratures which arise frequently in quantum chemistry, as well as to the determination of rigorous error bounds for the quality of approximate wavefunctions and the associated quantum-mechanical properties /2/.
KeywordsDeterminantal Equation Partitioning Technique Block Component Rigorous Bound Inhomogeneous Linear Equation
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