With the promotion by both mathematics itself and the practical requirements from modern society,the interest of studies on inverse problems and ill-posed problems,at home and abroad,has been flourishing in recent dec...With the promotion by both mathematics itself and the practical requirements from modern society,the interest of studies on inverse problems and ill-posed problems,at home and abroad,has been flourishing in recent decades.The intrinsic mathematical reasons for the studies on inverse problems come from the fact that most of the inverse problems are ill-posed,i.e.,the existence,uniqueness and stability of the solution cannot be ensured due to the configurations of the problems themselves.The characteristic of the ill-posedness for inverse problems makes it hard to construct the(generalized)solutions,especially to keep the solutions stable with respect to the noisy input data.To overcome these difficulties,some regularizing techniques should be introduced,which are closely related to many mathematical branches such as partial differential equations(PDEs),functional analysis,optimizations and numerical analysis.展开更多
文摘With the promotion by both mathematics itself and the practical requirements from modern society,the interest of studies on inverse problems and ill-posed problems,at home and abroad,has been flourishing in recent decades.The intrinsic mathematical reasons for the studies on inverse problems come from the fact that most of the inverse problems are ill-posed,i.e.,the existence,uniqueness and stability of the solution cannot be ensured due to the configurations of the problems themselves.The characteristic of the ill-posedness for inverse problems makes it hard to construct the(generalized)solutions,especially to keep the solutions stable with respect to the noisy input data.To overcome these difficulties,some regularizing techniques should be introduced,which are closely related to many mathematical branches such as partial differential equations(PDEs),functional analysis,optimizations and numerical analysis.
