This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin to the projected Landweber algorithm is studied. This work extends recent progress made on the efficient inversion of finite dimensional linear systems under...

where S is the Landweber-Novikov algebra. S has the added advantage of being a cocommutative Hopf algebra over Z. This paper does not remove this difficulty, but we will show that the monoid of multiplicative operations in BP*BP, (i.e. those operations which induce ring endomorphisms on BP*X for any space X)9 which we will denote by Γ{BP), has a submonoid analogous to the monoid of multiplicati...

The Landweber method is a simple and flexible iterative regularization algorithm, whose projected variant provides nonnegative image reconstructions. Since the method is usually very slow, we apply circulant preconditioners, exploiting the shift invariance of many deblurring problems, in order to accelerate the convergence. This way reasonable reconstructions can be obtained within few iteratio...

In this paper, the inverse problem for identifying initial value of time-fractional diffusion wave equation on spherically symmetric region is considered. The exact solution obtained by using method separating variables and property Mittag–Leffler functions. This ill-posed, i.e. solution(if exists) does not depend measurable data. Three different kinds landweber iterative methods are used to so...

We describe the structure of coefficient ring $$W^*(pt)=\varOmega_W^*$$ $$c_1$$ -spherical bordism theory for an arbitrary $$SU$$ -bilinear multiplication. prove that any multiplication formal group $$W^*$$ is Landweber exact. Also we show after inverting set $$\mathcal{P}$$ Fermat primes there exists a complex orientation localized $$W^*[\mathcal{P}^{-1}]$$ such coefficients corresponding law ...

– Peter Landweber had an invaluable contribution to these notes. First, by reading the final manuscript carefully, chasing potential mistakes and omissions. Second, by making many suggestions to improve the exposition locally. Unfortunately, he came to know the existence of the book only after it was sent to press, therefore his feedback only made it to these notes so far—perhaps they will make...

Over the last decades the theory of automata on infinite objects has been an important source of tools for the specification and the verification of computer programs. Trees are more suitable than words to model nondeterminism and concurrency. In the literature, there are several examples of acceptance conditions that have been proposed for automata on infinite words and then have been fruitful...

In this paper we shall be concerned with the construction of an adaptive Landweber iteration for solving linear ill-posed and inverse problems. Classical Landweber iteration schemes provide in combination with suitable regularization parameter rules order optimal regularization schemes. However, for many applications the implementation of Landweber’s method is numerically very intensive. Theref...