A class of hybrid heterogeneous methods using time implicit backward differences and Crank-Nicolson approximating schemes in conjunction with explicit domain decomposition approximate inverse matrix techniques is introduced for computing various families of approximate inverses based on approximate LU-type factorization techniques. Explicit preconditioned conjugate gradient type schemes in conj...

An adaptive multi-scale conjugate gradient method for distributed parameter estimations (or inverse problems) of wave equation is presented. The identification of the coefficients of wave equations in two dimensions is considered. First, the conjugate gradient method for optimization is adopted to solve the inverse problems. Second, the idea of multi-scale inversion and the necessary conditions...

The search direction in unconstrained minimization algorithms for large scale problems is usually computed as an iterate of the (precondi-tioned) conjugate gradient method applied to the minimization of a local quadratic model. In line-search procedures this direction is required to satisfy an angle condition, that says that the angle between the negative gradient at the current point and the d...