Semi-Infinite Linear Regression and Its Applications

Finite linear least squares is one of the core problems numerical algebra, with countless applications across science and engineering. Consequently, there a rich ongoing literature on algorithms for solving problems. In this paper, we explore variant in which system's matrix has infinite dimension (i.e., it quasimatrix). We call such semi-infinite regression As show, case arises several applications, supervised learning function approximation, allows novel interpretations existing algorithms. rigorously algorithmically. To that end, give formal framework working quasimatrices, generalize designed finite problem to case. Finally, suggest use various sampling methods obtaining an approximate solution.