MuPAD — A Summary

Fuchssteiner, Benno; Gottheil, Klaus; Kemper, Andreas; Kluge, Oliver; Morisse, Karsten; Naundorf, Holger; Oevel, Gudrun; Schulze, Thorsten; Wiwianka, Waldemar

doi:10.1007/978-3-0348-7335-2_3

Cited by 3 publications

(4 citation statements)

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“…All Bayes linear computations were carried out using the Bayes linear computing package, [B/D], available from [11]. The covariance calculations were carried out using the REDUCE computer algebra system, described in [7], and the MuPAD computer algebra system, described in [2] and [12]. The data for the example was provided by Positive Concepts Ltd.…”

Section: Acknowledgementsmentioning

confidence: 99%

Bayes Linear Variance Adjustment for Locally Linear DLMs

Wilkinson

1997

J. Forecast.

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This paper exhibits quadratic products of linear combinations of observables which identify the covariance structure underlying the univariate locally linear time series dynamic linear model. The ®rst-and second-order moments for the joint distribution over these observables are given, allowing Bayes linear learning for the underlying covariance structure for the time series model. An example is given which illustrates the methodology and highlights the practical implications of the theory. In Wilkinson and Goldstein (1996), new methodology is developed for the revision of covariance structures underlying two-step invertible dynamic linear models (DLMs). Two-step invertible DLMs are essentially models without a trend component. Here, the locally linear DLM will be discussed, which does have a trend component, and so is not two-step invertible. Interest will be focused on univariate DLMs, since it is simpler to explain the theory in the univariate context. However, a full covariance matrix approach may be taken to the multivariate counterpart, thus generalizing the work in Wilkinson and Goldstein (1996). It will be shown how one may learn about the three dierent kinds of variance associated with the locally linear dynamic linear model, using partial prior speci®cation for certain aspects of the model. The theory will be applied to the modelling of sales of a particular product from a wholesale depot, and the importance of good estimation of all of the variance components will be demonstrated in the context of this example.Ã Correspondence to:

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Section: Acknowledgementsmentioning

confidence: 99%

Bayes Linear Variance Adjustment for Locally Linear DLMs

Wilkinson

1997

J. Forecast.

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“…Some preliminary results for specific algorithms are reported in [13,29,26]. For parallel shared memories machines few librariea exist, which parallelize high level algorithms and use sequential arith-metic [20]. To our knowledge, only one package has been developed for vector computers [3].…”

Section: Basic Algorithmsmentioning

confidence: 99%

Calypso

Cesari

1997

Proceedings of the Second International Symposium on Parallel Symbolic Computation - PASCO '97

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We present a package of parallel algorithms for multiple precision arithmetic, implemented by using a mesaagepassing model of computation.These algorithms are organized in an object oriented library and perform parallel arithmetic in Z, Q, and ZP.The library hss a layered structure which provides ports bility and the possibility of extending the code e=ily. In the bottom layer we implement fundamental parallel algorithms which are machine dependent. Starting from integer mu]triplication, we developed different parallel Karatsub&type and FFT-b=ed schemes, including the integer 3-primes and floating-point FFT algorithms. These multiplication algorithms allowed us to design a pamllel Newton method for division. Parallel algorithms for modular arithmetic result by using both Montgomery's and classical arithmetic.We designed these algorithms under a messag~passing model of computation.These are implemented on different parallel platforms, targeting both distributed memory machhes, such as mwiively parallel processing systems and networks of workst ations, and shared memory architectures. We developed both architecture dependent and architecture independent algorithms by using standard interfaces such as the Message Passing Interface, MPI.On top of this layer we provide a convenient interface to the user which allows a sequential programming style, whale each algorithm is executed in parallel. At this level it is possible for the user to implement high level parallel algorithms, such m the GCD, which are machine independent.Finally we integrated our package in a computer algebra system, which uses a sequential frontend for interactive use, and a parallel backend for computation.We have called this package CALYPSO, a sort of acronym for computer Algebru Libmry for Pamllel Symbolic Computation.Permission to make digital/hard copy of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication and its date appear, and notice is given that copying is by permission of ACM, Inc. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. PASCO'97, Wailea, Maui, Hawaii; @1997 ACM 0-89791-951-3/97/0007. . .US$3.50 ComputationThe motivation of our work, that is writing a package for parallel multiple precision arithmetic, originates from a more general instance d~igning and implementing a parallel computer algebra system to solve practical problems which are still intractable with the existing software. We are thinkingof problems such as integer and polynomial factorization, Grobner basis computation, symbolic solution of large systems of equations, solution of differential equations. These problems are definitely not solved either by general purpose systems such as MATHEMATICAL [43] or MAPLE [12], nor by dedicated systems. On the other hand, with the lat@ advances in parallel computer hardware, the large amo...

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“…Hier ist natürlich ein ständiger Übergang zu beobachten, sei es, daß Spezialsysteme immer mehr allgemeinere Aufgaben erfüllen müssen und Strukturen benötigen, die dann eingebaut werden, oder umgekehrt, daß mit Hilfe etwa von Anwenderpaketen ein Allzwecksystem sehr wohl sehr spezielle Aufgaben lösen kann. 21 …”

Section: Spezielle Systemeunclassified

“…Eine gewisse Ausnahme bildet (noch) AXIOM, das sich noch auf dem Weg vom Großrechner über die Workstation -für die meisten Plattformen hier gibt es Versionen -bis zum PC befindet. Die Beispielrechnungen dieser Arbeit wurden aber bereits mit einer α-Version auf einem Laptop gerechnet 21. Ich beobachte auch mit etwas Sorge die Tendenz gerade in Deutschland, daß jede Arbeitsgruppe sich ihr eigenes System bastelt.…”

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Computeralgebra - eine Säule* des Wissenschaftlichen Rechnens / Computer-Algebra - a Part of the Foundation of Scientific Computing

Grabmeier¹

1995

it - Information Technology

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MuPAD — A Summary

Cited by 3 publications

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Bayes Linear Variance Adjustment for Locally Linear DLMs

Bayes Linear Variance Adjustment for Locally Linear DLMs

Calypso

Computeralgebra - eine Säule* des Wissenschaftlichen Rechnens / Computer-Algebra - a Part of the Foundation of Scientific Computing

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