Saeed Karimi

A variant of conjugate gradient type methods, called weighted conjugate gradient (WCG), is given to solve quadrature discretization of various first kind Fredholm integral equations with continuous kernels. The WCG type methods use a new inner product instead of the Euclidean one arising from discretization of L2-inner product by the quadrature formula. On this basis, the proposed algorithms generate a sequence of vectors which are approximations of solution at the quadrature points. Numerical experiments on a few model problems are used to illustrate the performance of the new methods compared to the CG type methods.