Index Calculus for Approximation Methods and Singular Value Decomposition

We introduce two classes of sequences An. of approximation operators, Moore]Penrose and Fredholm sequences, which correspond in a sense to normally solvable and Fredholm operators, respectively. For Moore]Penrose sequences, we derive a certain qualitative behavior of the singular values of the approximation operators An, and we describe this behavior quantitatively for Fredholm sequences by defining the a-number and the index of an approximation method