A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special tec...A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special technique of only storing non-zero elements is carried out. The incomplete LU factorization without fill-ins is adopted to reduce the condition number of the coefficient matrix. The BiCGSTAB algorithm is extended from the real system to the complex system and it is used to solve the preconditioned complex linear equations. The locked-rotor state of a single-sided linear induction machine is simulated by the software programmed with the finite element method and the PBiCGSTAB algorithm. Then the results are compared with those from the commercial software ANSYS, showing the validation of the proposed software. The iterative steps required for the proposed algorithm are reduced to about one-third, when compared to the BiCG method, therefore the algorithm is fast.展开更多
The current paper is mainly devoted to construct a generalized symbolic Thomas algorithm that will never fail. Two new efficient and reliable computational algorithms are given. The algorithms are suited for implement...The current paper is mainly devoted to construct a generalized symbolic Thomas algorithm that will never fail. Two new efficient and reliable computational algorithms are given. The algorithms are suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. Some illustrative examples are given.展开更多
为了使低密度奇偶校验码(Low Density Parity-check Code,LDPC)的校验矩阵H满足系统码的形式,同时降低校验矩阵的复杂度,减少编码时的存储空间,提出改进的优化准则,设计一种基于LU分解的算法。通过用全主元策略对校验矩阵进行高斯消元...为了使低密度奇偶校验码(Low Density Parity-check Code,LDPC)的校验矩阵H满足系统码的形式,同时降低校验矩阵的复杂度,减少编码时的存储空间,提出改进的优化准则,设计一种基于LU分解的算法。通过用全主元策略对校验矩阵进行高斯消元、行列交换等调整,使之具有系统码的形式,分解后得到的矩阵具有更好的稀疏性,从而可以进一步简化编码设计、减小存储空间占用和降低计算复杂度。所采用的算法与校验矩阵的构造无关,对性能无影响,且利于硬件实现,具有较好的应用前景。展开更多
The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a ser...The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a series of recursive relationships then we use them for constructing a novel algorithm for inverting a k-heptadiagonal matrix.The computational cost of the algorithm is calculated.Some illustrative examples are given to demonstrate the effectiveness of the proposed method.展开更多
文摘A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special technique of only storing non-zero elements is carried out. The incomplete LU factorization without fill-ins is adopted to reduce the condition number of the coefficient matrix. The BiCGSTAB algorithm is extended from the real system to the complex system and it is used to solve the preconditioned complex linear equations. The locked-rotor state of a single-sided linear induction machine is simulated by the software programmed with the finite element method and the PBiCGSTAB algorithm. Then the results are compared with those from the commercial software ANSYS, showing the validation of the proposed software. The iterative steps required for the proposed algorithm are reduced to about one-third, when compared to the BiCG method, therefore the algorithm is fast.
文摘The current paper is mainly devoted to construct a generalized symbolic Thomas algorithm that will never fail. Two new efficient and reliable computational algorithms are given. The algorithms are suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. Some illustrative examples are given.
文摘为了使低密度奇偶校验码(Low Density Parity-check Code,LDPC)的校验矩阵H满足系统码的形式,同时降低校验矩阵的复杂度,减少编码时的存储空间,提出改进的优化准则,设计一种基于LU分解的算法。通过用全主元策略对校验矩阵进行高斯消元、行列交换等调整,使之具有系统码的形式,分解后得到的矩阵具有更好的稀疏性,从而可以进一步简化编码设计、减小存储空间占用和降低计算复杂度。所采用的算法与校验矩阵的构造无关,对性能无影响,且利于硬件实现,具有较好的应用前景。
文摘The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a series of recursive relationships then we use them for constructing a novel algorithm for inverting a k-heptadiagonal matrix.The computational cost of the algorithm is calculated.Some illustrative examples are given to demonstrate the effectiveness of the proposed method.
