Simulating image coaddition with the Nancy Grace Roman Space Telescope: III. Software improvements and new linear algebra strategies

The Nancy Grace Roman Space Telescope will implement a devoted weak gravitational lensing program with its High Latitude Wide Area Survey. For cosmological purposes, a critical step in Roman image processing is to combine dithered undersampled images into unified oversampled images and thus enable high-precision shape measurements. IMCOM is an image coaddition algorithm which offers control over point spread functions in output images. This paper presents the refactored IMCOM software, featuring full object-oriented programming, improved data structures, and alternative linear algebra strategies for determining coaddition weights. Combining these improvements and other acceleration measures, to produce almost equivalent coadded images, the consumption of core-hours has been reduced by about an order of magnitude. We then re-coadd a $16 \times 16 \,{\rm arcmin}^2$ region of our previous image simulations with three linear algebra kernels in four bands, and compare the results in terms of IMCOM optimization goals, properties of coadded noise frames, and measurements of simulated stars. The Cholesky kernel is efficient and relatively accurate, yet its irregular windows for input pixels slightly bias coaddition results. The iterative kernel avoids this issue by tailoring input pixel selection for each output pixel; it yields better noise control, but can be limited by random errors due to finite tolerance. The empirical kernel coadds images using an empirical relation based on geometry; it is inaccurate, but being much faster, it provides a valid option for "quick look" purposes. We fine-tune IMCOM hyperparameters in a companion paper.