<Para ID="Par1">We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97–118, <CitationRef CitationID="CR8">2008</CitationRef>), Chen and Li (Appl Math Comput 170:686–705, <CitationRef CitationID="CR9">2005</CitationRef>), Chen and Li (Appl Math Comput 324:1381–1394, <CitationRef CitationID="CR10">2006</CitationRef>), Ferreira (J Comput Appl Math 235:1515–1522, <CitationRef CitationID="CR12">2011</CitationRef>), Ferreira and Gonçalves (Comput Optim Appl 48:1–21, <CitationRef CitationID="CR13">2011</CitationRef>), Ferreira and Gonçalves (J Complex 27(1):111–125, <CitationRef CitationID="CR14">2011</CitationRef>), Li et al. (J Complex 26:268–295, <CitationRef CitationID="CR19">2010</CitationRef>), Li et al. (Comput Optim Appl 47:1057–1067, <CitationRef CitationID="CR20">2004</CitationRef>), Proinov (J Complex 25:38–62, <CitationRef CitationID="CR22">2009</CitationRef>), Ewing, Gross, Martin (eds.) (The merging of disciplines: new directions in pure, applied and computational mathematics 185–196, <CitationRef CitationID="CR23">1986</CitationRef>), Traup (Iterative methods for the solution of equations, <CitationRef CitationID="CR24">1964</CitationRef>), Wang (J Numer Anal 20:123–134, <CitationRef CitationID="CR25">2000</CitationRef>), we provide a larger radius of convergence; tighter error estimates on the distances involved and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost. Copyright Springer Science+Business Media New York 2015
