地震层析成像中LSQR算法的快速求解
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摘要
针对传统LSQR反演算法计算时间长、占用内存大的不足,这里提出了一种LSQR的快速算法,通过线性三元组存储稀疏矩阵,实现相应的矩阵运算,使LSQR算法的运算速度及内存占用都有较大地改善。
In this paper,we propose a new LSQR calculation method,which uses a triad table to store sparse matrix,and all matrix operation is based on the triad table.Compared with traditional LSQR method,this method is more superior in the respect of both computing time and memory consumption.
In this paper,we propose a new LSQR calculation method,which uses a triad table to store sparse matrix,and all matrix operation is based on the triad table.Compared with traditional LSQR method,this method is more superior in the respect of both computing time and memory consumption.
引文
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[11]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.
[12]吴律.层析基础及其在井间地震中的应用[M].北京:石油工业出版社,1997.
[13]PAIGE C C,SAYBDERS M A.LSQR:Sparse linear e-quations and least squares problems[J].ACM Transac-tions on Mathematical Software,1982,8(2):195.
[14]PAIGE C C,SAUNDERS M A.LSQR An algorithm forsparse linear equations and sparse least squares[J].ACM Transactions on Mathematical Software,1982,8(1):43.
[15]飞思科技产品研发中心.MATLAB 6.5应用接口编程[M].北京:电子工业出版社,2003.
[2]HESTENES M R,STEIFEL E.Methods of conjugate gra-dients for solving linear systems[J].J.Res.Nat.Bur.Standards,1952(49i6):409.
[3]OWE AXELSSON.Solution of linear systems of equa-tions:Iterative methods,Sparse Matrix Techniques[M].Lecture Notes in Mathematics,Springer Berlin/Heidel-berg,1977.
[4]LANCZOS C.An iteration method for the solution of theeigenvalue problem of linear differential and integral op-erators[J].J.Res.Nat.Bur.Standards,1950(45):255.
[5]SAUNDERS M A.Solution of sparse rectangular systemsusing LSQR and CRAIG[J].BIT,1995(35):588.
[6]GUUST NOLET.Seismic Tomography:With Applicationsin Global Seismology and Exploration Geophysics[M].Published by Springer,1987.
[7]张贤达.矩阵分析与应用[M].北京:清华大学出版社,2004.
[8]JENNINGS A.Matrix Computations for Engineers andscientists[M].John-Wiley and Sons,1977.
[9]GENE H.Golub,Charles F.Van Loan,Matrix Computa-tions[M].The Johns Hopkins University Press,1996.
[10]徐树方.矩阵计算的理论与方法[M].北京:北京大学出版社,1995.
[11]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.
[12]吴律.层析基础及其在井间地震中的应用[M].北京:石油工业出版社,1997.
[13]PAIGE C C,SAYBDERS M A.LSQR:Sparse linear e-quations and least squares problems[J].ACM Transac-tions on Mathematical Software,1982,8(2):195.
[14]PAIGE C C,SAUNDERS M A.LSQR An algorithm forsparse linear equations and sparse least squares[J].ACM Transactions on Mathematical Software,1982,8(1):43.
[15]飞思科技产品研发中心.MATLAB 6.5应用接口编程[M].北京:电子工业出版社,2003.
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