TY - JOUR A2 - Mahmudov, Nazim I. AU - Wireko, Fredrick Asenso AU - Barnes, Benedict AU - Sebil, Charles AU - Ackora-Prah, Joseph PY - 2021 DA - 2021/11/26 TI - The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems SP - 4373290 VL - 2021 AB - This paper shows that discrete linear equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, banded matrix operator, TST matrix operator, and sparse matrix operator are ill-posed in the sense of Hadamard. Gauss least square method (GLSM), QR factorization method (QRFM), Cholesky decomposition method (CDM), and singular value decomposition (SVDM) failed to regularize these ill-posed problems. This paper introduces the eigenspace spectral regularization method (ESRM), which solves ill-posed discrete equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, and banded and sparse matrix operator. Unlike GLSM, QRFM, CDM, and SVDM, the ESRM regularizes such a system. In addition, the ESRM has a unique property, the norm of the eigenspace spectral matrix operator κK=K1K=1. Thus, the condition number of ESRM is bounded by unity, unlike the other regularization methods such as SVDM, GLSM, CDM, and QRFM. SN - 1110-757X UR - https://doi.org/10.1155/2021/4373290 DO - 10.1155/2021/4373290 JF - Journal of Applied Mathematics PB - Hindawi KW - ER -