Fredholm第一种积分方程Ax=y的表示定理和一次迭代定理*
Representation Theorem and One-Iteration Theorem for Fredholm Integral Equation of the First Kind Ax=y
-
摘要: 本文给出两个定理.表示定理指出:若具有界L2核的Fredholm第一种积分方程Ax=y有唯一解,则其中,一次迭代定理指出:可由公式=x0+g0A*(y-Ax0)一次迭代求得的充分和必要条件是满足下列条件之一:Abstract: In this paper, two theorems are presented. The representation theorem stales: if the Fredholm integral equation of the first kind Ax=y, with bounded L2 kernel, has a uniquesolution , Then ,where .The one-iteration theorem states: can be achieved in one iteration by =x0+g0A*(y-Ax0)if one of the following conditions is satisfied:
-
[1] Mueller,P.F.and G.O.Reynolds,Image resloration by removal of random media degradations,J.Opt.Soc.Amer.,57(1967),1338-1344. [2] Andrews,H.C.,A.H.Tescher,and R.P.Kruger,Image processing by digital computer,IEEE Spectrum,2(1972),20-32. [3] Liskovec,O.A.,Regularization of ill posed problems and a connection with the method of quasi solution,Differencial'nye Uravmcnija,5(1969),1836-1847. [4] Liht,M.K.,The solution of minimizing a quadratic functional with approximate data,Z.Uycial.Nat.i Mat.Fiz.,19(1969),1004-1014. [5] Yun Tian-quan,Uniqueness theorem of non-singular itegral equation method,Transactions CSME,10(1986),197-200. [6] Yun Tian-quan,An integral equation method for solving the torsion problem of revolution bodies,J.H.I.T.,1(1979),82-97. MR 81m;73028. [7] 袁家乐,回转体一旋旋桨组合体之推力减额的一个数值预测方法,中国造船,87(1984)14-21. [8] Yun Tian-quan,Pile analysis by simple integral equation method,Appl.Math.& Mech.,2,3(1981),331-348. MR 83i:73014. [9] Pogorzelski,W.,Integral Equations and Their Applications,Vol.1,Pergamon Press,PWN-Polish Scientific Publishers(1966). [10] Landweber,L.,An iteration formula for Fredholm integral equations of the first kind,Amer.J.Math.,73(1951),615-624. [11] Diaz,J.B.and F.T.Metcalf,On iteration procedures for equations of the first kind,Ax=y,and Picard's criterion for the existence of a solution,Math.Comput.,24(1970),923-935. [12] 云天铨,Fredholm第一种积分方程Ax=y的最速迭代解法,华中工学院学报,3 (1978),94-98. [13] Smithies,F.,Integral Equations,Cambridge University Press(1956). [14] Stakgold,I.,Green's Functions and Boundary Value Problems,John Wiley & Sons,New York(1979). [15] Baker,C.T.H.,The numerical treatment of integral equations,Clarendon Press,Oxford(1977).
点击查看大图
计量
- 文章访问数: 1774
- HTML全文浏览量: 48
- PDF下载量: 403
- 被引次数: 0