Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Matrix_chain_multiplication> ?p ?o }
Showing triples 1 to 54 of
54
with 100 triples per page.
- Matrix_chain_multiplication abstract "Matrix chain multiplication (or Matrix Chain Ordering Problem, MCOP) is an optimization problem that can be solved using dynamic programming. Given a sequence of matrices, the goal is to find the most efficient way to multiply these matrices. The problem is not actually to perform the multiplications, but merely to decide the sequence of the matrix multiplications involved.We have many options because matrix multiplication is associative. In other words, no matter how we parenthesize the product, the result obtained will remain the same. For example, if we had four matrices A, B, C, and D, we would have:((AB)C)D = ((A(BC))D) = (AB)(CD) = A((BC)D) = A(B(CD)).However, the order in which we parenthesize the product affects the number of simple arithmetic operations needed to compute the product, or the efficiency. For example, suppose A is a 10 × 30 matrix, B is a 30 × 5 matrix, and C is a 5 × 60 matrix. Then,(AB)C = (10×30×5) + (10×5×60) = 1500 + 3000 = 4500 operationsA(BC) = (30×5×60) + (10×30×60) = 9000 + 18000 = 27000 operations.Clearly the first method is more efficient. With this information, the problem statement can be refined, how do we determine the optimal parenthesization of a product of n matrices? We could go through each possible parenthesization (brute force), requiring a run-time that is exponential in the number of matrices, which is very slow and impractical for large n. A quicker solution to this problem can be achieved by breaking up the problem into a set of related subproblems. By solving subproblems one time and reusing these solutions, we can drastically reduce the run-time required. This concept is known as dynamic programming.".
- Matrix_chain_multiplication wikiPageID "1538007".
- Matrix_chain_multiplication wikiPageLength "14758".
- Matrix_chain_multiplication wikiPageOutDegree "24".
- Matrix_chain_multiplication wikiPageRevisionID "700469412".
- Matrix_chain_multiplication wikiPageWikiLink Associative_property.
- Matrix_chain_multiplication wikiPageWikiLink Binary_operation.
- Matrix_chain_multiplication wikiPageWikiLink Bracket_(mathematics).
- Matrix_chain_multiplication wikiPageWikiLink Brute-force_search.
- Matrix_chain_multiplication wikiPageWikiLink C_(programming_language).
- Matrix_chain_multiplication wikiPageWikiLink Catalan_number.
- Matrix_chain_multiplication wikiPageWikiLink Category:Dynamic_programming.
- Matrix_chain_multiplication wikiPageWikiLink Category:Matrices.
- Matrix_chain_multiplication wikiPageWikiLink Category:Optimization_algorithms_and_methods.
- Matrix_chain_multiplication wikiPageWikiLink Concatenation.
- Matrix_chain_multiplication wikiPageWikiLink Dynamic_programming.
- Matrix_chain_multiplication wikiPageWikiLink Hexagon.
- Matrix_chain_multiplication wikiPageWikiLink Linked_list.
- Matrix_chain_multiplication wikiPageWikiLink Matrix_multiplication.
- Matrix_chain_multiplication wikiPageWikiLink Memoization.
- Matrix_chain_multiplication wikiPageWikiLink Polygon_triangulation.
- Matrix_chain_multiplication wikiPageWikiLink Recursion.
- Matrix_chain_multiplication wikiPageWikiLink Reduction_(complexity).
- Matrix_chain_multiplication wikiPageWikiLink Regular_polygon.
- Matrix_chain_multiplication wikiPageWikiLink Time_complexity.
- Matrix_chain_multiplication wikiPageWikiLink Top-down_and_bottom-up_design.
- Matrix_chain_multiplication wikiPageWikiLink File:Catalan-Hexagons-example.svg.
- Matrix_chain_multiplication wikiPageWikiLink File:Matrix_chain_multiplication_polygon_example.svg.
- Matrix_chain_multiplication wikiPageWikiLinkText "Matrix chain multiplication".
- Matrix_chain_multiplication wikiPageWikiLinkText "matrix chain multiplication".
- Matrix_chain_multiplication wikiPageWikiLinkText "matrix chain ordering".
- Matrix_chain_multiplication wikiPageUsesTemplate Template:Expand_section.
- Matrix_chain_multiplication subject Category:Dynamic_programming.
- Matrix_chain_multiplication subject Category:Matrices.
- Matrix_chain_multiplication subject Category:Optimization_algorithms_and_methods.
- Matrix_chain_multiplication hypernym Problem.
- Matrix_chain_multiplication type Disease.
- Matrix_chain_multiplication type Algorithm.
- Matrix_chain_multiplication type Matrix.
- Matrix_chain_multiplication type Method.
- Matrix_chain_multiplication comment "Matrix chain multiplication (or Matrix Chain Ordering Problem, MCOP) is an optimization problem that can be solved using dynamic programming. Given a sequence of matrices, the goal is to find the most efficient way to multiply these matrices. The problem is not actually to perform the multiplications, but merely to decide the sequence of the matrix multiplications involved.We have many options because matrix multiplication is associative.".
- Matrix_chain_multiplication label "Matrix chain multiplication".
- Matrix_chain_multiplication sameAs Q917612.
- Matrix_chain_multiplication sameAs ضرب_سلسلة_مصفوفات.
- Matrix_chain_multiplication sameAs Matrix-Kettenmultiplikation.
- Matrix_chain_multiplication sameAs ضرب_زنجیرهای_ماتریس.
- Matrix_chain_multiplication sameAs Problem_nawiasowania_ciągu_macierzy.
- Matrix_chain_multiplication sameAs m.058wsf.
- Matrix_chain_multiplication sameAs Задача_о_порядке_перемножения_матриц.
- Matrix_chain_multiplication sameAs Множење_ланаца_матрица.
- Matrix_chain_multiplication sameAs Q917612.
- Matrix_chain_multiplication sameAs 矩陣鏈乘積.
- Matrix_chain_multiplication wasDerivedFrom Matrix_chain_multiplication?oldid=700469412.
- Matrix_chain_multiplication isPrimaryTopicOf Matrix_chain_multiplication.
