INDEX CALCULUS FOR APPROXIMATION METHODS AND SINGULAR-VALUE DECOMPOSITION

We introduce two classes of sequences (A(n)) of approximation operator s, Moore-Penrose and Fredholm sequences, which correspond in a sense t o normally solvable and Fredholm operators, respectively. For Moore-Pe nrose sequences, we derive a certain qualitative behavior of the singu lar values of the approximation operators A(n), and we describe this b ehavior quantitatively for Fredholm sequences by defining the alpha-nu mber and the index of an approximation method. (C) 1998 Academic Press .