# Melman, Aaron

Publications

[1] A.Ben-Tal, A.Melman and J.Zowe, "Curved search methods for unconstrained optimization", Optimization, 21 (1990), 669-695.

[2] A.Melman, "A new linesearch method for quadratically constrained convex programming", Operations Research Letters, 16 (1994), 67-77.

[3] A.Melman, "Numerical Solution of a Secular Equation", Numerische Mathematik, 69 (1995), 483-493.

[4] A.Melman and R.Polyak, "The Newton modified barrier method for QP problems", Annals of Operations Research, 62 (1996), 465-519.

[5] A.Melman, "A linesearch procedure in barrier methods for some convex programming problems", SIAM J. of Optimization, 6 (1996), 283-298.

[6] A.Melman, "A unifying convergence analysis of second-order methods for secular equations", Mathematics of Computation, 66 (1997), 333-344.

[7] A.Melman, "Geometry and convergence for Euler's and Halley's methods", SIAM Review, 39 (1997), 728-735.

[8] A.Melman, "Analysis of higher-order methods for secular equations", Mathematics of Computation, 67 (1997), 271-286.

[9] A.Melman, "A numerical comparison of methods for solving secular equations", Journal of Computational and Applied Mathematics, 86 (1997), 237-249.

[10] A.Melman, "Spectral functions for real symmetric Toeplitz matrices", Journal of Computational and Applied Mathematics, 98 (1998), 233-243.

[11] A.Melman, "Bounds on the extreme eigenvalues of real symmetric Toeplitz matrices", SIAM J. on Matrix Analysis and Applications, 21 (1999), 362-378.

[12] A.Melman, "A symmetric algorithm for Toeplitz systems", Linear Algebra and its Applications, 301 (1999), 145-152.

[13] A.Melman and G. Rabinowitz, "Efficient methods for a class of continuous nonlinear knapsack problems", SIAM Review, 42 (2000), 440-448.

[14] A.Melman, "A recurrence relation for real symmetric Toeplitz matrices", IEEE Transactions on Signal Processing, 48 (2000), 1829-1831.

[15] A.Melman, "Symmetric centrosymmetric matrix-vector multiplication", Linear Algebra and its Applications, 320 (2000), 193-198.

[16] A.Melman, "Extreme eigenvalues of symmetric positive definite Toeplitz matrices", Mathematics of Computation, 70 (2001), 649-669.

[17] A.Melman, "The even-odd split Levinson algorithm for Toeplitz systems", SIAM J. on Matrix Analysis and Applications, 23 (2001), 256-270.

[18] A.Melman, "A two-step even-odd split Levinson algorithm for Toeplitz systems", Linear Algebra and its Applications, 338 (2001), 219-237.

[19] A.Melman, "Computation of the smallest even and odd eigenvalues of a symmetric positive-definite Toeplitz matrix", SIAM J. on Matrix Analysis and Applications, 25 (2004), 947-963.

[20] A.Melman, "Computation of the Newton step for the even and odd characteristic polynomials of a symmetric positive-definite Toeplitz matrix", Mathematics of Computation, 75 (2006), 817-832.

[21] A.Melman and W.B.Gragg, "An optimization framework for polynomial zerofinders", American Mathematical Monthly, 113 (2006), 794-804.

[22] A.Melman, "A bug problem", College Mathematics Journal, May 2006 issue, 219-221.

[23] A.Melman, "Double-step Newton for polynomials with all real zeros", Applied Mathematics Letters, 20 (2007), 671-675.

[24] A.Melman, "Bounds on the zeros of the derivative of a polynomial with all real zeros", American Mathematical Monthly, 115 (2008), pp. 145-147.

[25] A.Melman, "Some properties of Newton's method for polynomials with all real zeros", Taiwanese Journal of Mathematics, 12 (2008), 2315-2325.

[26] A.Melman, "Overshooting properties of Newton-like and Ostrowski-like methods", American Mathematical Monthly, 116 (2009), 238-250.

[27] T.S.Carothers and A.Melman, "More bounds on the location of critical points of a polynomial with all real zeros", Pi Mu Epsilon Journal, 13 (2009), 13-20.

[28] A.Melman, "Spectral inclusion sets for structured matrices", Linear Algebra and its Applications, 431 (2009), 633-656.

[29] A.Melman, "An alternative to the Brauer set", Linear and Multilinear Algebra, 58 (2010), 377-385.

[30] A.Melman, "Fractional double Newton step properties for polynomials with all real zeros", Matematicki Vesnik, 62 (2010), 1-9.

[31] A.Melman, "Generalizations of Gershgorin disks and polynomial zeros", Proceedings of the American Mathematical Society, 138 (2010), 2349-2364.

[32] A.Melman, "Gershgorin disk fragments", Mathematics Magazine, 83 (2010), 123-129.

[33] A.Melman, "A pseudo Laguerre method", Matematicki Vesnik, 663 (2011), 295-304.

[34] A.Melman, "Modified Gershgorin disks for companion matrices", SIAM Review, 54 (2012), 355-373.

[35] A.Melman, "Ovals of Cassini for Toeplitz matrices", Linear and Multilinear Algebra, 60 (2012), 189-199.

[36] A.Melman, "Geometry of trinomials", Pacific Journal of Mathematics, 259 (2012), 141-159.

[37] A.Melman, "A single oval Oval of Cassini for the zeros of a polynomial", Linear and Multilinear Algebra, 61 (2013), 183-195.

[38] A.Melman, "Upper and lower bounds for the Perron root of a nonnegative matrix", Linear and Multilinear Algebra, 61 (2013), 171-181.

[39] A.Melman, "Comment on a result by Alpin, Chien, and Yeh", Proceedings of the American Mathematical Society, 141 (2013), 775-779.

[40] A.Melman, "The twin of a theorem by Cauchy", American Mathematical Monthly, 120 (2013), 164-168.

[41] A.Melman, "A somewhat unexpected concavity", The Teaching of Mathematics, 16 (2013), 18-21.

[42] A.Melman, "A geometric maximization problem", The Teaching of Mathematics, 16 (2013), 35-41.

[43] A.Melman, "Generalization and variations of Pelletís theorem for matrix polynomials", Linear Algebra and its Applications, 439 (2013), 1550-1567.

[44] A.Melman, "Inclusion disks for polynomial zeros in generalized bases", Linear Algebra and its Applications, 445 (2014), 326-346.

[45] A.Melman, "Implementation of Pellet's theorem", Numerical Algorithms, 65 (2014), 293-304.

[46] A.Melman, "Cauchy-type inclusion and exclusion regions for polynomial zeros", The Teaching of Mathematics, 17 (2014), 39-50.

[47] A.Melman, "Nonscalar matrix polynomial representation of some scalar polynomials", Linear Algebra and its Applications, 474 (2015), 141-157.

[48] A.Melman, "Geometric aspects of Pellet's and related theorems", Rocky Mountain Journal of Mathematics, 45 (2015), 603-621.

[49] A.Melman, "On Pellet's theorem for a class of lacunary polynomials", Mathematics of Computation, 85 (2016), 707-716.

[50] A.Melman, "Bounds for eigenvalues of matrix polynomials with applications to scalar polynomials", Linear Algebra and its Applications, 504 (2016), 190-203.

[51] A.Melman, "Cauchy-like and Pellet-like results for polynomials", Linear Algebra and its Applications, 505 (2016), 174-193.

[52] A.Melman, "Improvement of Pellet's theorem for scalar and matrix polynomials", Comptes Rendus Math. Acad. Sci. Paris, 8 (2016), 859-863.