Rational approximation of n j-r using ladder arithmetic (with computer program)

• Main Authors: Nalangan, Ana Marissa L., Sinlao, Rowena A.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Approximation theory; Arithmetic functions; Numbers, Theory of; Programming (Mathematics); Polynomials
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16172
• Institution: De La Salle University

This thesis introduces the method of ladder approximation which uses basic operations to obtain rational approximation of n j/r where n is a real number greater than 1 but not necessarily an integer, j and r are positive integers ( j r).The ladder representation of n j/r is in the form of a rectangular array satisfying three properties. The main result of this paper is that as one proceeds down the ladder, the quotients of the entries in various columns with those of the first column approach the powers of the rth roof of n. Also, a computer program is designed to aid the computations involved in approximating n j/r. However, the value of n, r, j are limited to 1 n 100, j r respectively due to memory and screen capacity of the computer.