Two algorithms are presented for finding a zero of a real continuous function defined on a given interval. The methods used are mixtures of linear interpolation, rational interpolation, and bisectmn. The asymptotic behavior of these algorithms is completely satisfactory. The munber of function evaluations needed to find a zero of a function is bounded byâ€¦ (More)

This paper considers elimination methods to solve dense linear systems, in particular a variant of Gaussian elimination due to Huard [13]. This variant reduces the system to an equivalent diagonal system just like Gauss-Jordan elimination, but does not require more floating-point operations than Gaussian elimination. To preserve stability, a pivotingâ€¦ (More)

This paper considers elimination methods to solve dense linear systems, in particular a variant due to Huard of Gaussian elimination [13]. This variant reduces the system to an equivalent diagonal system just as GaussJordan elimination, but does not require more floating-point operations than Gaussian elimination. Huard's method may be advantageous for useâ€¦ (More)

This paper presents algorithms for calculating the quadratic character and the norms of prime ideals in the ring of integers of any quadratic field. The norms of prime ideals are obtained by means of a sieve algorithm using the quadratic character for the field considered. A quadratic field, and its ring of integers, can be represented naturally in a plane.â€¦ (More)

This paper presents an algorithm for calculating prime numbers in quadratic elds having the unique factorization property. The algorithm resembles the sieve algorithm of Eratosthenes to determine the primes in the set of natural numbers. Quadratic elds are chosen because they can be represented naturally in a plane. Using this representation, the primes ofâ€¦ (More)