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| Description
| - The computational efficiency of the sparse-matrix LU factorization represents the key point of the computer-aided design of electronic circuits. The LU factorization must be performed thousand times during the numerical solution of systems of nonlinear differential-algebraic equations, which further enhances importance of this problem. Moreover, the sparse matrix of the system is always irregular here - hence, the methods that are generally available for regular ones cannot be used. We created a novel modification of the Markowitz criterion, which is compatible with the so-called fast modes of the LU factorization. The modified criterion consists in an estimation of probabilities of the fill-in enlargement. The probabilities are determined for all columns of the system matrix before the LU factorization, where the column probability is calculated as the average value of the probabilities of its elements. Finally, the columns are reordered so that first and last ones should be those with the minimal and maximal probabilities, respectively. As a verification of the proposed algorithm, a comprehensive set of numerical tests has been carried out. This algorithm and another one that uses the column weights directly were successfully implemented to our C.I.A. (Circuit Interactive Analyzer) program, and the two versions were compared (both are much better than the unsorted algorithm). As this topic is very important for the VLSI circuit design, we published our first experimental results at a top-ranking world symposium: IEEE International Conference on Very Large Scale Integration, Oct 2011, Hong Kong. (In this paper, 23 various circuits were tested; now, we have a comparison of more than 50 ones.) Another problem consists in the accuracy of the large-scale computations. This problem was also resolved by using the variable-length arithmetics or functional LISP language, which was described in a detailed way in a paper in Radioengineering, Dec 2011 (current WoS IF=0.739).
- The computational efficiency of the sparse-matrix LU factorization represents the key point of the computer-aided design of electronic circuits. The LU factorization must be performed thousand times during the numerical solution of systems of nonlinear differential-algebraic equations, which further enhances importance of this problem. Moreover, the sparse matrix of the system is always irregular here - hence, the methods that are generally available for regular ones cannot be used. We created a novel modification of the Markowitz criterion, which is compatible with the so-called fast modes of the LU factorization. The modified criterion consists in an estimation of probabilities of the fill-in enlargement. The probabilities are determined for all columns of the system matrix before the LU factorization, where the column probability is calculated as the average value of the probabilities of its elements. Finally, the columns are reordered so that first and last ones should be those with the minimal and maximal probabilities, respectively. As a verification of the proposed algorithm, a comprehensive set of numerical tests has been carried out. This algorithm and another one that uses the column weights directly were successfully implemented to our C.I.A. (Circuit Interactive Analyzer) program, and the two versions were compared (both are much better than the unsorted algorithm). As this topic is very important for the VLSI circuit design, we published our first experimental results at a top-ranking world symposium: IEEE International Conference on Very Large Scale Integration, Oct 2011, Hong Kong. (In this paper, 23 various circuits were tested; now, we have a comparison of more than 50 ones.) Another problem consists in the accuracy of the large-scale computations. This problem was also resolved by using the variable-length arithmetics or functional LISP language, which was described in a detailed way in a paper in Radioengineering, Dec 2011 (current WoS IF=0.739). (en)
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| Title
| - Enhanced Types of Algorithms for Sparse-Matrix LU Factorization With Suppressed Fill-In and Improved Accuracy
- Enhanced Types of Algorithms for Sparse-Matrix LU Factorization With Suppressed Fill-In and Improved Accuracy (en)
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| skos:prefLabel
| - Enhanced Types of Algorithms for Sparse-Matrix LU Factorization With Suppressed Fill-In and Improved Accuracy
- Enhanced Types of Algorithms for Sparse-Matrix LU Factorization With Suppressed Fill-In and Improved Accuracy (en)
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| skos:notation
| - RIV/68407700:21230/12:00204680!RIV13-MSM-21230___
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...onomickeParametry
| - Při řešení rozsáhlých úloh v elektrotechnice, ekonomice, astronomii apod. s využitím LU faktorizace úspora paměti, ale především strojního času v řádu desítek až stovek procent oproti dostupným algoritmům.
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/68407700:21230/12:00204680
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| http://linked.open...terniIdentifikace
| - SLUF Version 3 '12 (FTN95, LISP)
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - LU Factorization; sparse matrices; computer-aided design; Markowitz criterion; VLSI; variable-length arithmetics; LISP (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open.../licencniPoplatek
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...echnickeParametry
| - Sparse-matrix LU factorization with suppressed fill-In and improved accuracy. Obecně použitelný algoritmus vhodný pro řešení jakýchkoliv velmi rozsáhlých soustav lineárních rovnic s nepravidelnou řídkou maticí soustavy. Licenci na zdrojový kód lze získat: ČVUT v Praze, K13137, Josef Dobeš, Technická 2, 16627 Praha 6, tel. 224352207, dobes@fel.cvut.cz
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| http://linked.open...iv/tvurceVysledku
| - Dobeš, Josef
- Černý, David
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| http://linked.open...avai/riv/vlastnik
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| http://linked.open...itiJinymSubjektem
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| http://localhost/t...ganizacniJednotka
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