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- Matrix_chain_multiplication abstract "Matrix chain multiplication is an optimization problem that can be solved using dynamic programming. Given a sequence of matrices, we want to find the most efficient way to multiply these matrices together. The problem is not actually to perform the multiplications, but merely to decide in which order to perform the multiplications.We have many options because matrix multiplication is associative. In other words, no matter how we parenthesize the product, the result will be the same. For example, if we had four matrices A, B, C, and D, we would have:(ABC)D = (AB)(CD) = A(BCD) = A(BC)D = ....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 the more efficient. Now that we have identified the problem, how do we determine the optimal parenthesization of a product of n matrices? We could go through each possible parenthesization (brute force), but this would require time exponential in the number of matrices, which is very slow and impractical for large n. The solution, as we will see, is to break up the problem into a set of related subproblems. By solving subproblems one time and reusing these solutions many times, we can drastically reduce the time required. This is known as dynamic programming.".
- Matrix_chain_multiplication thumbnail Catalan-Hexagons-example.svg?width=300.
- Matrix_chain_multiplication wikiPageExternalLink dynamic-programming-matrix-multiplication.
- Matrix_chain_multiplication wikiPageExternalLink tpds03.pdf.
- Matrix_chain_multiplication wikiPageExternalLink 268391.html.
- Matrix_chain_multiplication wikiPageExternalLink matrixchainorder.
- Matrix_chain_multiplication wikiPageExternalLink whitepapers.html.
- Matrix_chain_multiplication wikiPageExternalLink Matrix.
- Matrix_chain_multiplication wikiPageExternalLink 27950.
- Matrix_chain_multiplication wikiPageID "1538007".
- Matrix_chain_multiplication wikiPageRevisionID "606717765".
- Matrix_chain_multiplication hasPhotoCollection Matrix_chain_multiplication.
- 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 type Abstraction100002137.
- Matrix_chain_multiplication type Act100030358.
- Matrix_chain_multiplication type Activity100407535.
- Matrix_chain_multiplication type Algorithm105847438.
- Matrix_chain_multiplication type Arrangement107938773.
- Matrix_chain_multiplication type Array107939382.
- Matrix_chain_multiplication type Event100029378.
- Matrix_chain_multiplication type Group100031264.
- Matrix_chain_multiplication type Matrices.
- Matrix_chain_multiplication type Matrix108267640.
- Matrix_chain_multiplication type OptimizationAlgorithmsAndMethods.
- Matrix_chain_multiplication type Procedure101023820.
- Matrix_chain_multiplication type PsychologicalFeature100023100.
- Matrix_chain_multiplication type Rule105846932.
- Matrix_chain_multiplication type YagoPermanentlyLocatedEntity.
- Matrix_chain_multiplication comment "Matrix chain multiplication is an optimization problem that can be solved using dynamic programming. Given a sequence of matrices, we want to find the most efficient way to multiply these matrices together. The problem is not actually to perform the multiplications, but merely to decide in which order to perform the multiplications.We have many options because matrix multiplication is associative. In other words, no matter how we parenthesize the product, the result will be the same.".
- Matrix_chain_multiplication label "Matrix chain multiplication".
- Matrix_chain_multiplication label "Matrix-Kettenmultiplikation".
- Matrix_chain_multiplication label "Problem nawiasowania ciągu macierzy".
- Matrix_chain_multiplication label "Задача о порядке перемножения матриц".
- Matrix_chain_multiplication label "ضرب سلسلة مصفوفات".
- Matrix_chain_multiplication label "矩陣鏈乘積".
- Matrix_chain_multiplication sameAs Matrix-Kettenmultiplikation.
- Matrix_chain_multiplication sameAs Problem_nawiasowania_ciągu_macierzy.
- Matrix_chain_multiplication sameAs m.058wsf.
- Matrix_chain_multiplication sameAs Q917612.
- Matrix_chain_multiplication sameAs Q917612.
- Matrix_chain_multiplication sameAs Matrix_chain_multiplication.
- Matrix_chain_multiplication wasDerivedFrom Matrix_chain_multiplication?oldid=606717765.
- Matrix_chain_multiplication depiction Catalan-Hexagons-example.svg.
- Matrix_chain_multiplication isPrimaryTopicOf Matrix_chain_multiplication.
