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Algebraic View Specification?
, 1996
"... The application of algebraic specification techniques in the early phases of software development requires a means for specifying views. In this paper we argue for algebraic view specification based on an algebraic concept model. The concept model consists of two parts: a meta model defining the con ..."
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Cited by 3 (1 self)
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The application of algebraic specification techniques in the early phases of software development requires a means for specifying views. In this paper we argue for algebraic view specification based on an algebraic concept model. The concept model consists of two parts: a meta model defining
An Algebraic View of Structural Induction
 Computer Science Logic 1994, number 933 in Lect. Notes Comp. Sci
, 1994
"... We propose a uniform, categorytheoretic account of structural induction for inductively defined data types. The account is based on the understanding of inductively defined data types as initial algebras for certain kind of endofunctors T : B !B on a bicartesian/distributive category B . Regarding ..."
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Cited by 10 (5 self)
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We propose a uniform, categorytheoretic account of structural induction for inductively defined data types. The account is based on the understanding of inductively defined data types as initial algebras for certain kind of endofunctors T : B !B on a bicartesian/distributive category B . Regarding
An Algebraic View of Combination Rules
, 1994
"... . Combining information from multiple sources is a topic of central importance for Uncertain Reasoning. In this paper we approach the problem of formulating appropriate Combination Rules for Uncertain Reasoning from an algebraic, latticetheoretical perspective. Our purpose is to state the problem o ..."
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Cited by 1 (1 self)
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. Combining information from multiple sources is a topic of central importance for Uncertain Reasoning. In this paper we approach the problem of formulating appropriate Combination Rules for Uncertain Reasoning from an algebraic, latticetheoretical perspective. Our purpose is to state the problem
DFT and FFT: An algebraic view
, 2009
"... In infinite, or nonperiodic, discretetime signal processing, there is a strong connection between the ztransform, Laurent series, convolution, and the discretetime Fourier transform (DTFT) [10]. As one may expect, a similar connection exists for the DFT but bears surprises. Namely, it turns out ..."
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that the proper framework for the DFT requires modulo operations of polynomials, which means working with socalled polynomial algebras [6]. Associated with polynomial algebras is the Chinese remainder theorem, which describes the DFT algebraically and can be used as a tool to concisely derive various FFTs
An Algebraic View on Recursive Types
 Applied Categorical Structures
, 1996
"... This paper is a translated extract of my diploma thesis, see [Mar95]. I would like to thank Pawe/l Urzyczyn for some useful hints, Martin Hofmann, Mathias Kegelmann and Hermann Puhlmann for their careful proof reading, and especially Achim Jung for his stimulating supervision ..."
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Cited by 2 (0 self)
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This paper is a translated extract of my diploma thesis, see [Mar95]. I would like to thank Pawe/l Urzyczyn for some useful hints, Martin Hofmann, Mathias Kegelmann and Hermann Puhlmann for their careful proof reading, and especially Achim Jung for his stimulating supervision
An algebraic view of program composition
 Algebraic Methodology and Software Technology, number 1548 in Lect. Notes Comp. Sci
, 1998
"... Abstract. We propose a general categorical setting for modeling program composition in which the callbyvalue and callbyname disciplines fit as special cases. Other notions of composition arising in denotational semantics are captured in the same framework: our leading examples are nondeterminist ..."
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Cited by 1 (0 self)
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Abstract. We propose a general categorical setting for modeling program composition in which the callbyvalue and callbyname disciplines fit as special cases. Other notions of composition arising in denotational semantics are captured in the same framework: our leading examples are nondeterministic callbyneed programs and nonstrict functions with side effects. Composition of such functions is treated in our framework with the same degree of abstraction that Moggi’s categorical approach based on monads allows in the treatment of callbyvalue programs. By virtue of such abstraction, interesting program equivalences can be validated axiomatically in mathematical models obtained by means of modular constructions. 1
An algebraic view of multidimensional . . .
, 2003
"... The problem of computing equalizers for multidimensional multipleinput multipleoutput (MIMO) finite impulse response (FIR) filters using MIMO FIR filters is considered. Prior results are reviewed establishing conditions for the equalizability of a given MIMO FIR filter and of a generic MIMO FIR f ..."
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The problem of computing equalizers for multidimensional multipleinput multipleoutput (MIMO) finite impulse response (FIR) filters using MIMO FIR filters is considered. Prior results are reviewed establishing conditions for the equalizability of a given MIMO FIR filter and of a generic MIMO FIR filter. Algorithms for the computation of MIMO FIR equalizers are derived and their relative strengths and weaknesses are discussed. A parametrization of the set of all equalizers for a given MIMO FIR filter is derived. Known bounds on the orders of the equalizer are doubly exponential in the order of the given MIMO FIR filter; alternative generic bounds are derived which are linear in the order of the given MIMO FIR filter, and the behavior of the bound for large number of outputs is characterized. A fast algorithm (generalizing the Levinson algorithm to the multidimensional case) is proposed for multidimensional Wiener filtering and for computing equalizers for singleinput multipleoutput (SIMO) systems. A minimal set of test targets is established for polarimetric calibration of ultrawide band synthetic aperture radar systems, and equalizer orders for
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
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Cited by 526 (72 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 672 (18 self)
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Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented by 200300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...
Flexible camera calibration by viewing a plane from unknown orientations
, 1999
"... We propose a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled ..."
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Cited by 512 (7 self)
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We propose a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closedform solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique, and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one step from laboratory environments to real world use. The corresponding software is available from the author’s Web page.
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