A new class of the structured matrices related to the discrete skew-self-adjoint Dirac systems is introduced. The corresponding matrix identities and inversion procedure are treated. Analogs of the Schur coefficients and of the Christoffel-Darboux formula are studied. It is shown that the structured matrices from this class are always positive-definite, and applications for an inverse problem f...

We present a computationally efficient and accurate adjoint method for calculating coupled sensitivities of complex frequency-domain excitation and emission fluence to any underlying optical parameters in highly scattering media. The method is shown to be general and accurate. Novel vectorized implementations for finite element global matrix assembly and adjoint sensitivity calculations are sho...

Amongst recent contributions to preconditioning methods for saddle point systems, standard iterative methods in nonstandard inner products have been usefully employed. Krzyżanowski (Numer. Linear Algebra Appl. 2011; 18:123–140) identified a two-parameter family of preconditioners in this context and Stoll and Wathen (SIAM J. Matrix Anal. Appl. 2008; 30:582–608) introduced combination preconditi...

On the half line [0,∞) we study first order differential operators of the form B 1 i d dx +Q(x), where B := ( B1 0 0 −B2 ) , B1, B2 ∈ M(n,C) are self–adjoint positive definite matrices and Q : R+ → M(2n,C), R+ := [0,∞), is a continuous self–adjoint off–diagonal matrix function. We determine the self–adjoint boundary conditions for these operators. We prove that for each such boundary value prob...

On the half line [0,∞) we study first order differential operators of the form B 1 i d dx +Q(x), where B := ( B1 0 0 −B2 ) , B1, B2 ∈ M(n,C) are self–adjoint positive definite matrices and Q : R+ → M(2n,C), R+ := [0,∞), is a continuous self–adjoint off–diagonal matrix function. We determine the self–adjoint boundary conditions for these operators. We prove that for each such boundary value prob...

By using the spherical coordinates in 3+1 dimensions we study the self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an infinitely thin magnetic flux tube. It is shown that the angular part of the Dirac Hamiltonian requires self-adjoint extensions as well as its radial one. The self-adjoint extensions of the angular part are parametrized by a 2 × 2 unitary matrix. ∗e-m...

1 Definition of the Adjoint Let V be a complex vector space with an inner product < , and norm , and suppose that L : V → V is linear. If there is a function L * : V → V for which Lx, y = x, L * y (1.1) holds for every pair of vectors x, y in V , then L * is said to be the adjoint of L. Some of the properties of L * are listed below. Proof. Introduce an orthonomal basis B for V. Then find the m...

TM2 is a global three-dimensional model of the atmospheric transport of passive tracers. The adjoint of TM2 is a model that allows the efficient evaluation of derivatives of the simulated tracer concentration at observational locations with respect to the tracer’s sources and sinks. We describe the generation of the adjoint model by applying the Tangent linear and Adjoint Model Compiler in the ...