In his 1999 SIGSAM BULLETIN paper [7], H. J. Stetter gave an explicit formula for finding the nearest polynomial with a given zero. This present paper revisits the issue, correcting a minor omission from Stetter's formula and explicitly extending the results to different polynomial bases.Experiments with our implementation demonstrate that the formula may not after all, fully solve the problem, and we discuss some outstanding issues: first, that the nearest polynomial with the given zero may be identically zero (which might be surprising), and, second, that the problem of finding the nearest polynomial of the same degree with a given zero may not, in fact, have a solution. A third variant of the problem, namely to find the nearest monic polynomial (given a monic polynomial initially) with a given zero, a problem that makes sense in some polynomial bases but not others, can also be solved with Stetter's formula, and this may be more satisfactory in some circumstances. This last can be generalized to the case where some coefficients are intrinsic and not to be changed, whereas others are empiric and may safely be changed. Of course, this minor generalization is implicit in [7]; This paper simply makes it explicit.

Purpose: In spite of over twenty years of computerized tomography (CT) research since the well‐known Feldkamp‐Davis‐Kress (FDK) method was first derived for three‐dimensional Cone‐Beam Computerized Tomographic (CBCT) reconstruction, there is a noticeable lack of practical software implementations available. Medical physics researchers needing CBCT reconstructions to prototype more advanced imaging techniques generally need to code the FDK method from scratch or adapt third‐party code that may be sophisticated and inflexible. To address this gap in free software tools, the AAPM Imaging Research Subcommittee has supported the development of OSCaR, a simple‐yet‐flexible open‐source Matlab FDK tool for algorithm development. Method and Materials: OSCaR includes open source, executable, and GUI software (Matlab; The MathWorks, Natick MA) for CBCT reconstructions from 2D projections. As a pre‐processing stage, projection data are parsed from a standard data‐file. Upon specification of a Field‐Of‐View (FOV), voxel size, and reconstruction filter, the 3D sinogram is filtered and back‐projected to produce a 3D reconstruction. The final reconstruction can be exported to various data formats as specified by the user. Results: OSCaR accepts data in a variety of formats accessible to Matlab. A circular source‐detector geometry is assumed, but OSCaR allows specification of the piercing point as a function of the projection angle. The aperture can be freely selected, as can the voxel size and the reconstruction filter. Visualization in 3D and in 2D (e.g., slices) is supported. Conclusion: OSCaR demonstrates flexibility, ease of use, and support of a broad range of input data formats. Upon completion of beta testing, the code will be freely available via the AAPM web‐site to AAPM members. The software is intended for algorithm development and research purposes rather than for clinical or commercial use. The software provides a reference‐able base of code to accelerate new imaging research in CBCT and facilitate multi‐institutional collaboration.

Abstract. Spectra and pseudospectra of matrix polynomials are of interest in geometric intersection problems, vibration problems, and analysis of dynamical systems. In this note we consider the effect of the choice of polynomial basis on the pseudospectrum and on the conditioning of the spectrum of regular matrix polynomials. In particular, we consider the direct use of the Lagrange basis on distinct interpolation nodes, and give a geometric characterization of "good" nodes. We also give some tools for computation of roots at infinity via a new, natural, reversal. The principal achievement of the paper is to connect pseudospectra to the well-established theory of Lebesgue functions and Lebesgue constants, by separating the influence of the scalar basis from the natural scale of the matrix polynomial, which allows many results from interpolation theory to be applied.

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