Charles Micchelli
Journal of Approximation Theory
We present a model for computation over the reals or an arbitrary (ordered) ring R. In this general setting, we obtain universal machines, partial recursive functions, as well as NP-complete problems. While our theory reflects the classical over Z (e.g., the computable functions are the recursive functions) it also reflects the special mathematical character of the underlying ring R (e.g., complements of Julia sets provide natural examples of R. E. undecidable sets over the reals) and provides a natural setting for studying foundational issues concerning algorithms in numerical analysis. © 1989 American Mathematical Society.
Charles Micchelli
Journal of Approximation Theory
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
R.B. Morris, Y. Tsuji, et al.
International Journal for Numerical Methods in Engineering
Tong Zhang, G.H. Golub, et al.
Linear Algebra and Its Applications