Alfred H. Morris

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An algorithm is given for evaluating the incomplete beta function ratio <italic>I<subscrpt>x</subscrpt>(a,b)</italic> and its complement <italic>1 - I<supscrpt>x</supscrpt>(a,b)</italic>. A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is(More)
An algorithm is given for computing the incomplete gamma function ratios <italic>P</italic>(<italic>a</italic>, <italic>x</italic>) and <italic>Q></italic>(<italic>a</italic>, <italic>x</italic>) for <italic>a</italic> &gne; 0, <italic>x</italic> &gne; 0, <italic>a</italic> + <italic>x</italic> &#8800; 0. Temme's uniform asymptotic expansions are used. The(More)
Authors’ address: U.S. Naval Surface Weapons Center, Dahlgren, VA 22448. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission(More)
In July 1980, the proposed final form of the Ada programming language was released by the U.S. Department of Defense [1]. Even though Ada was not designed specifically for general numeric scientific computation, nevertheless the question arises to whether it is appropriate for this purpose. This question can best be answered by consideration of the(More)
The effect of increasing systemic blood pressure on retinal blood flow was investigated in anaesthetised miniature pigs. Blood pressure was increased by the infusion of the sympathomimetic amine, tyramine. Volume flow was determined from axial erythrocyte velocity, measured by laser Doppler velocimetry, and vessel diameter, measured from monochromatic(More)
In this paper various algebraic properties of the indefinite Riemann integral that are appropriate for its use on the computer are examined. From this analysis it is seen that the operation of the integral on certain simply described families of functions, called invariant algebras, indicates how it must also act on more complex families of maps. Several(More)
The purpose of this paper is to describe and illustrate a program, written for the IBM 7090, which defines a model for a finite collection of algebras for the computer. It is shown that the program contains a structure broad enough in scope to allow one to perform operations on such diverse mathematical concepts as differential equations, infinite series,(More)
PURPOSE There are multiple factors that have lead to the need for an increased precision and accuracy in Radiation Therapy. The increased use of IMRT and SBRT with hypofractionated doses requires optimal precision and accuracy in aligning the treatment delivery with the target. Recent advances in imaging and motion management of patients during the(More)
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