Representation Theorem and One-Iteration Theorem for Fredholm Integral Equation of the First Kind Ax=y

Yun Tian-quan

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1989 > 10(7): 569-574

Yun Tian-quan. Representation Theorem and One-Iteration Theorem for Fredholm Integral Equation of the First Kind Ax=y[J]. Applied Mathematics and Mechanics, 1989, 10(7): 569-574.

Citation:

Yun Tian-quan. Representation Theorem and One-Iteration Theorem for Fredholm Integral Equation of the First Kind Ax=y[J]. Applied Mathematics and Mechanics, 1989, 10(7): 569-574.

Citation:

Yun Tian-quan. Representation Theorem and One-Iteration Theorem for Fredholm Integral Equation of the First Kind Ax=y[J]. Applied Mathematics and Mechanics, 1989, 10(7): 569-574.

PDF( 362 KB)

Representation Theorem and One-Iteration Theorem for Fredholm Integral Equation of the First Kind Ax=y

Yun Tian-quan

Department of Engineering Mechanics, South China University of Technology, Guangzhou

Received Date: 1988-04-05
Publish Date: 1989-07-15

Abstract

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:

FullText(HTML)

References(15)

References

[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).