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RfA113 349STANFORD
UNIV CA DEPT OF COMPUTER
SCIENCEUnNCLASSIFIEDCOMPUTATION OF MATRIX CHAIN PRODUCTS. PART I, PART IL.(U)
SEP 81 T C HU. M T SHINS
DAAG2980C0029
STANCS81875
AR16323.2M
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How to fill out computation of matrix chain
How to fill out computation of matrix chain
01
Identify the number of matrices in the chain and assign them numerical indices.
02
Determine the dimensions (rows and columns) of each matrix.
03
Create a table to store the optimal multiplication order and cost.
04
Initialize the diagonal entries of the table with zeros.
05
Iterate over the diagonal entries of the table, starting from the bottom left.
06
For each entry in the diagonal, consider all possible split points to divide the chain into two subchains.
07
Calculate the cost of multiplying the subchains using the formula: cost = table[split_point][i] + table[i+1][split_point+1] + dimensions[split_point] * dimensions[i+1] * dimensions[split_point+1+1].
08
Update the table entry with the minimum cost found in step 7.
09
Continue iterating over the diagonal until reaching the top right corner of the table.
10
The optimum cost of multiplying the entire matrix chain is stored in the top right corner of the table.
11
Backtrack through the table to determine the optimal multiplication order.
12
Print or store the optimal multiplication order and cost.
Who needs computation of matrix chain?
01
Computation of matrix chain is required in various fields such as computer graphics, image processing, numerical simulations, and optimization problems.
02
It is specifically useful in algorithms that involve repeated matrix multiplications, such as dynamic programming algorithms and linear algebra computations.
03
Researchers, engineers, and programmers working in these domains can benefit from understanding and implementing the computation of matrix chain to optimize their algorithms and improve efficiency.
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What is computation of matrix chain?
Computation of matrix chain refers to the process of determining the most efficient way to multiply a given sequence of matrices together. It involves finding the optimal parenthesization of the matrices to minimize the total number of scalar multiplications.
Who is required to file computation of matrix chain?
Typically, individuals or organizations involved in operations that require matrix multiplication, particularly in computational mathematics or computer graphics, may need to compute matrix chain multiplication. However, it is not a fileable requirement in legal or financial contexts.
How to fill out computation of matrix chain?
To fill out a computation of matrix chain, one must identify the dimensions of the matrices involved and apply dynamic programming techniques to calculate the minimum number of multiplications needed. This includes creating a table to document the costs and parenthesization.
What is the purpose of computation of matrix chain?
The purpose of computation of matrix chain is to optimize the process of multiplying a chain of matrices, which can be computationally expensive, by minimizing the number of operations required.
What information must be reported on computation of matrix chain?
It typically includes the dimensions of each matrix, the order of multiplication, the computed costs for each multiplication, and the optimal parenthesization of the matrices.
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