Di Fiore, Carmine; Fanelli, Stefano; Lepore, Filomena; Zellini, Paolo Matrix algebras in quasi-Newton methods for unconstrained minimization. (English) Zbl 1034.65045 Numer. Math. 94, No. 3, 479-500 (2003). The authors describe a new class of quasi-Newton methods for unconstrained minimization problems. The matrix used in the recursion process is defined as the best Frobenius norm least-squares fit of the classical well known choice in quasi-Newton methods, by a special algebra of matrices simultaneously diagonalized by a unitary fast Fourier transform. The method requires \({\mathcal{O}}(n\log n)\) flops per iteration and \({\mathcal{O}}(n)\) memory allocations. Convergence and computational complexity are also analysed for the classes of methods described in the paper. Reviewer: Constantin Popa (Constanta) Cited in 2 ReviewsCited in 13 Documents MSC: 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 90C53 Methods of quasi-Newton type Keywords:quasi-Newton methods; unconstrained minimization; Frobenius norm; fast Fourier transform; Frobenius norm least-squares fit; convergence; computational complexity Software:L-BFGS-B; L-BFGS PDFBibTeX XMLCite \textit{C. Di Fiore} et al., Numer. Math. 94, No. 3, 479--500 (2003; Zbl 1034.65045) Full Text: DOI