Tabular representation of multivariate functions—with applications to topographic modeling

<italic>The data compression problem</italic> One of the outstanding problems confronting computer users is compact representation of functions of more than one variable. Most storage-limited computer programs devote a major part of their available memory to the representation of functions of more than one variable: e.g., equation-of-state tables in physics problems,<supscrpt>1</supscrpt> optimal return functions in dynamic-programming problems,<supscrpt>2</supscrpt> routing tables in communications simulations,<supscrpt>3</supscrpt> tables of manpower and material in simulations of military theatre operation,<supscrpt>4</supscrpt> function representation in meteorological and astronomical investigations,<supscrpt>5</supscrpt> and representation of topographic information. This paper develops and analyzes tabular methods with respect to the topographic representation problem. However, the result are presented in terms of general smoothness and accuracy parameters; thus, they also apply to the other problems mentioned above.