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Backward Substitution

The Experts below are selected from a list of 1554 Experts worldwide ranked by ideXlab platform

Saeed Jafarzadeh – 1st expert on this subject based on the ideXlab platform

  • An analytical approach for solving type-1 and type-2 fully fuzzy linear systems of equations
    2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016
    Co-Authors: Sheriff Sadiqbatcha, Saeed Jafarzadeh

    Abstract:

    A general analytical method for solving fully fuzzy linear system (FFLSE) of equations using interval analysis and LU decomposition is proposed in this study. Both type-1 and interval type-2 fuzzy coefficients are discussed. Alpha level sets (alpha cuts) are used to reduce a FFLSE into a number of interval systems, which are then solved systematically using LU decomposition and forward-Backward Substitution. To carry out forward-Backward Substitution on interval equations, conditions for the existence and uniqueness of interval solutions are derived and approximations are used for cases when an interval solution does not exist. The proposed method is then extended to solve interval type-2 fuzzy system of equations.

  • FUZZ-IEEE – An analytical approach for solving type-1 and type-2 fully fuzzy linear systems of equations
    2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016
    Co-Authors: Sadiqbatcha, Saeed Jafarzadeh

    Abstract:

    A general analytical method for solving fully fuzzy linear system (FFLSE) of equations using interval analysis and LU decomposition is proposed in this study. Both type-1 and interval type-2 fuzzy coefficients are discussed. Alpha level sets (alpha cuts) are used to reduce a FFLSE into a number of interval systems, which are then solved systematically using LU decomposition and forward-Backward Substitution. To carry out forward-Backward Substitution on interval equations, conditions for the existence and uniqueness of interval solutions are derived and approximations are used for cases when an interval solution does not exist. The proposed method is then extended to solve interval type-2 fuzzy system of equations.

Sheriff Sadiqbatcha – 2nd expert on this subject based on the ideXlab platform

  • An analytical approach for solving type-1 and type-2 fully fuzzy linear systems of equations
    2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016
    Co-Authors: Sheriff Sadiqbatcha, Saeed Jafarzadeh

    Abstract:

    A general analytical method for solving fully fuzzy linear system (FFLSE) of equations using interval analysis and LU decomposition is proposed in this study. Both type-1 and interval type-2 fuzzy coefficients are discussed. Alpha level sets (alpha cuts) are used to reduce a FFLSE into a number of interval systems, which are then solved systematically using LU decomposition and forward-Backward Substitution. To carry out forward-Backward Substitution on interval equations, conditions for the existence and uniqueness of interval solutions are derived and approximations are used for cases when an interval solution does not exist. The proposed method is then extended to solve interval type-2 fuzzy system of equations.

Jiayi Du – 3rd expert on this subject based on the ideXlab platform

  • A Hybrid Parallel Tridiagonal Solver on Multi-core Architectures
    2014 IEEE International Parallel & Distributed Processing Symposium Workshops, 2014
    Co-Authors: Guangping Tang, Kenli Li, Keqin Li, Hang Chen, Jiayi Du

    Abstract:

    An optimized parallel algorithm is proposed to solve the problem occurred in the process of complicated Backward Substitution of cyclic reduction during solving tridiagonal linear systems. Adopting a hybrid parallel model, this algorithm combines the cyclic reduction method and the partition method. This hybrid algorithm has simple Backward Substitution on parallel computers comparing with the cyclic reduction method. In this paper, the operation count and execution time are obtained to evaluate and make comparison for these methods. On the basis of results of these measured parameters, the hybrid algorithm using the hybrid approach with a multi-threading implementation achieves better efficiency than the other parallel methods, i.e., the cyclic reduction and the partition methods. Among them, the cyclic reduction method is previously found to be the fastest algorithm in many ways for solutions. In particular, the approach involved in this paper has the least scalar operation count and the shortest execution time on multi-core computer when the size of an equation is large enough. The hybrid parallel algorithm improves the performance of the cyclic reduction and partition methods by 30% and 20% respectively.

  • IPDPS Workshops – A Hybrid Parallel Tridiagonal Solver on Multi-core Architectures
    2014 IEEE International Parallel & Distributed Processing Symposium Workshops, 2014
    Co-Authors: Guangping Tang, Kenli Li, Keqin Li, Hang Chen, Jiayi Du

    Abstract:

    An optimized parallel algorithm is proposed to solve the problem occurred in the process of complicated Backward Substitution of cyclic reduction during solving tridiagonal linear systems. Adopting a hybrid parallel model, this algorithm combines the cyclic reduction method and the partition method. This hybrid algorithm has simple Backward Substitution on parallel computers comparing with the cyclic reduction method. In this paper, the operation count and execution time are obtained to evaluate and make comparison for these methods. On the basis of results of these measured parameters, the hybrid algorithm using the hybrid approach with a multi-threading implementation achieves better efficiency than the other parallel methods, i.e., the cyclic reduction and the partition methods. Among them, the cyclic reduction method is previously found to be the fastest algorithm in many ways for solutions. In particular, the approach involved in this paper has the least scalar operation count and the shortest execution time on multi-core computer when the size of an equation is large enough. The hybrid parallel algorithm improves the performance of the cyclic reduction and partition methods by 30% and 20% respectively.