Home/Algebra/Least squares/Least-squares problem22. Least squaresLeast-squares problemLevel: avanzadoIn 22. Least squaresFormulaCopy LaTeXx^=argminx∥Ax−b∥22\hat x=\arg\min_x\|Ax-b\|_2^2x^=argxmin∥Ax−b∥22Tagsalgebraalgebra formulalinearleast squaresDetailSeeks the best approximation when Ax=b has no exact solution.Explore the ideaFound an error? Contact us.Related formulasRelatedOrthogonal projectionprojb(a)=a⋅b∥b∥2b\operatorname{proj}_b(a)=\frac{a\cdot b}{\|b\|^2}bprojb(a)=∥b∥2a⋅bbOpen formulaOpen in sectionRelatedNormal equationsATAx^=ATbA^TA\hat x=A^TbATAx^=ATbOpen formulaOpen in section