SOLVING LARGE FULL SETS OF LINEAR EQUATIONS ON A MICROCOMPUTER.
Item
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Title
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SOLVING LARGE FULL SETS OF LINEAR EQUATIONS ON A MICROCOMPUTER.
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Identifier
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AAI8629748
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identifier
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8629748
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Creator
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THURM, JOSEPH.
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Contributor
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Pat Sterbenz
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Date
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1986
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Language
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English
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Publisher
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City University of New York.
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Subject
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Computer Science
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Abstract
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The solution of Ax = b, where the entire matrix A cannot fit into RAM, is examined. Various methods are presented for partitioning A into submatrices, which are then stored on disk until needed. Based on the partitioning scheme, algorithms decomposing A into LU factors are developed and analyzed. Since these algorithms do explicit disk reads and writes for the submatrices of A, the selection of algorithm which does the least of the I/O is of paramount importance.;The row storage method stores several complete rows together in a submatrix, so the original matrix A is viewed as an array of blocks. The maximum size of each block is approximately one-half of available memory. Since all the decomposition algorithms for this storage method require two blocks to be in memory at once, the row storage method assumes that at least two complete rows will fit into memory at once.;The column storage method stores several complete columns together in a submatrix, so the matrix A is viewed as a vector of blocks. Again, the maximum size of each block is approximately one-half of available memory, and all the decomposition algorithms for this storage method require that at least two complete columns will fit into memory at once.;The submatrix storage method divides A into a matrix of square blocks. This storage method does not require two complete rows or columns to fit into memory at once. Some of the decomposition algorithms require that three blocks be in memory at once, limiting the size of a block to one-third of memory. Other decomposition algorithms only require two blocks to be in memory at once, allowing the blocks to grow to one-half memory.;Based on the amount of memory available and the dimensions of A, the storage method and associated decomposition algorithm which do the least amount of I/O are determined from the results presented.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Computer Science
