TY - JOUR
TI - Kaczmarz algorithm revisited
AU - Sznajder, Roman
TI - Kaczmarz algorithm revisited
AB - 
	In 1937, Stefan Kaczmarz proposed a simple method, called the Kaczmarz algorithm, to solve iteratively systems of linear equations Ax = b in Euclidean spaces. This procedure employs cyclic orthogonal projections onto the hyperplanes associated with such a system. In the case of a nonsingular matrix A, Kaczmarz showed that his method guarantees convergence to the solution of Ax = b. The Kaczmarz algorithm was rediscovered in 1948 and became an important tool in medical engineering. We briefly discuss generalizations of this method and its ramifications, including applications in computer tomography, image processing and contemporary harmonic analysis.
VL - 2015
IS - Fundamental Sciences Issue 2-NP (20) 2015
PY - 2016
SN - 0011-4561
C1 - 2353-737X
SP - 247
EP - 254
DO - 10.4467/2353737XCT.15.220.4425
UR - https://ejournals.eu/en/journal/czasopismo-techniczne/article/kaczmarz-algorithm-revisited
KW - Kaczmarz method
KW - systems of linear equations
KW - computer tomography
KW - image reconstruction