Recent years have been characterized by the increasing amountofpublications in...Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics ofwhich the first...more
Recent years have been characterized by the increasing amountofpublications in...Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics ofwhich the first...more
Iteration regularization i.e. utilization of iteration methods of any form for...Iteration regularization i.e. utilization of iteration methods of any form for the stable approximate solution of ill-posed problems is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In...more
Many problems in science technology and engineering are posed in the form of o...Many problems in science technology and engineering are posed in the form of operator equations of the first kind with the operator and RHS approximately known. But such problems often turn out to be ill-posed having no solution or a non-unique...more
Recent years have been characterized by the increasing amountofpublications in...Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics ofwhich the first...more
The book covers fundamentals of the theory of optimal methods for solving ill-...The book covers fundamentals of the theory of optimal methods for solving ill-posed problems as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a...more
The theory of ill-posedproblems originated in an unusual way. As a rule a new...The theory of ill-posed problems originated in an unusual way. As a rule a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are...more
Iteration regularization i.e. utilization of iteration methods of any form for...Iteration regularization i.e. utilization of iteration methods of any form for the stable approximate solution of ill-posed problems is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In...more
Many problems in science technology and engineering are posed in the form of o...Many problems in science technology and engineering are posed in the form of operator equations of the first kind with the operator and RHS approximately known. But such problems often turn out to be ill-posed having no solution or a non-unique...more
As a rule many practical problems are studied in a situation when the input da...As a rule many practical problems are studied in a situation when the input data are incomplete. For example this is the case for a parabolic partial differential equation describing the non-stationary physical process of heat and mass transfer if...more
1. Interpolation problems play an important role both in theoretical and appli...1. Interpolation problems play an important role both in theoretical and applied investigations. This explains the great number of works dedicated to classical and new interpolation problems ([1)-[5] [8) [13)-[16] [26)-[30] [57]). In this book we...more
Unlike most elementary books on matrices A Combinatorial Approach to Matrix Th...Unlike most elementary books on matrices A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory shedding new light on the subject by exploring the...more
Classicalexamples of moreand more oscillatingreal-valued functions on a domain...Classicalexamples of moreand more oscillatingreal-valued functions on a domain N ?of R are the functions u (x)=sin(nx)with x=(x ... x ) or the so-called n 1 1 n n+1 Rademacherfunctionson]0 1[ u (x)=r (x) = sgn(sin(2 x))(seelater3.1.4). n n They may...more
The book covers fundamentals of the theory of optimal methods for solving ill-...The book covers fundamentals of the theory of optimal methods for solving ill-posed problems as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a...more
The first formulations of linear boundary value problems for analytic function...The first formulations of linear boundary value problems for analytic functions were due to Riemann (1857). In particular such problems exhibit as boundary conditions relations among values of the unknown analytic functions which have to be...more