skip to content
Formulation of linear problems and solution by a universal machine Preview this item
ClosePreview this item
Checking...

Formulation of linear problems and solution by a universal machine

Author: B Curtis Eaves; Uriel G Rothblum
Publisher: [S.l.] : DIMACS, Center for Discrete Mathematics and Theoretical Computer Science, [1992]
Series: DIMACS technical report, 92-42.
Edition/Format:   Book : English
Database:WorldCat
Summary:
Abstract: "Using the predicate language for ordered fields we define a class of problems to which we refer as linear problems. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the rank-computation of matrices, the testing of whether sets that are defined by
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Document Type: Book
All Authors / Contributors: B Curtis Eaves; Uriel G Rothblum
OCLC Number: 29907162
Notes: "September, 1992."
Description: 83 p. : ill. ; 28 cm.
Series Title: DIMACS technical report, 92-42.
Responsibility: by B. Curtis Eaves and Uriel G. Rothblum.

Abstract:

Abstract: "Using the predicate language for ordered fields we define a class of problems to which we refer as linear problems. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the rank-computation of matrices, the testing of whether sets that are defined by linear inequalities are semi-lattices, all satisfiability problems in sentenial logic, all problems of determining complete simplices on a complex and all quadratic programming problems with bounded variables and all problems of computing row-reduced echelon forms of matrices.

We describe a single, one, method, to which we refer as the Univeral Linear Machine, which can be used to solve any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates an ordered field algorithm for the problem. Then, given an instance of the linear problem, in the second phase the ordered field algorithm solves the particular instance of the linear problem. The ordered field algorithm is finite, deterministic, loopless and executes only the five ordered field operations -- additions, multiplications, subtractions, divisions and comparisons.

Conversely, we show that for each ordered field algorithm there is a linear problem which the ordered field algorithm solves uniquely. Finally, it is shown that with an ordered field algorithm for a linear problem, one can solve certain parametric instances of the linear problem."

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Related Subjects:(1)

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


<http://www.worldcat.org/oclc/29907162>
library:oclcnum"29907162"
library:placeOfPublication
owl:sameAs<info:oclcnum/29907162>
rdf:typeschema:Book
schema:about
schema:about
schema:contributor
schema:creator
schema:datePublished"1992"
schema:description"Conversely, we show that for each ordered field algorithm there is a linear problem which the ordered field algorithm solves uniquely. Finally, it is shown that with an ordered field algorithm for a linear problem, one can solve certain parametric instances of the linear problem.""@en
schema:description"Abstract: "Using the predicate language for ordered fields we define a class of problems to which we refer as linear problems. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the rank-computation of matrices, the testing of whether sets that are defined by linear inequalities are semi-lattices, all satisfiability problems in sentenial logic, all problems of determining complete simplices on a complex and all quadratic programming problems with bounded variables and all problems of computing row-reduced echelon forms of matrices."@en
schema:description"We describe a single, one, method, to which we refer as the Univeral Linear Machine, which can be used to solve any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates an ordered field algorithm for the problem. Then, given an instance of the linear problem, in the second phase the ordered field algorithm solves the particular instance of the linear problem. The ordered field algorithm is finite, deterministic, loopless and executes only the five ordered field operations -- additions, multiplications, subtractions, divisions and comparisons."@en
schema:exampleOfWork<http://worldcat.org/entity/work/id/31803807>
schema:inLanguage"en"
schema:name"Formulation of linear problems and solution by a universal machine"@en
schema:numberOfPages"83"
schema:publisher
schema:url

Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.