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Clenshaw-Curtis quadrature is a particularly important automatic quadrature scheme for a variety of reasons, especially the high accuracy obtained from relatively few integrand values. However, it has received little use because it requires the computation of a cosine transformation, and the...
We have programmed and made timing comparisons for two algorithms which sample the multivariate normal density N ( ॖ , V ) = | V -1 |/(2ॠ) n /2 · exp (- 1/2( Y - ॖ ) T V -1 ( Y - ॖ )) (1) where V is an n X n covariance matrix, ॖ is an n component vector of means, and Y is an n...
Clenshaw-Curtis quadrature is one of the most effective automatic quadrature schemes available, particularly for integrands with some continuous derivatives. It can also be used for any piecewise continuous integrand, although it is not recommended for integrands with discontinuities.
This paper presents an approach to writing specifications for parts of software systems. The main goal is to provide specifications sufficiently precise and complete that other pieces of software can be written to interact with the piece specified without additional information. The secondary...
Sorting by means of a two-way merge has a reputation of requiring a clerically complicated and cumbersome program. This ALGOL 60 procedure demonstrates that, using recursion, an elegant and efficient algorithm can be designed, the correctness of which is easily proved 2. Sorting n objects gives...
In a companion paper to this, “I Methodology and Experiences,” the automatic Clenshaw-Curtis quadrature scheme was described and how each quadrature formula used in the scheme requires a cosine transformation of the integrand values was shown. The high cost of these cosine transformations has...
As experience with use of on-line operating systems has grown, the need to share information among system users has become increasingly apparent. Many contemporary systems permit some degree of sharing. Usually, sharing is accomplished by allowing several users to share data via input and output...
This algorithm implements the Hu-Tucker method of variable length, minimum redundancy alphabetic binary encoding 1. The symbols of the alphabet are considered to be an ordered forest of n terminal nodes. Two nodes in an ordered forest are said to be tentative-connecting if the sequence of nodes...
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