Steepest Descent Method

An Algorithm for calculating the Gradient of a function at an -D point .The steepest descent method starts at a point and, as many times as needed, moves from to by minimizing along the line extending from in the direction of ,the local downhill gradient. This method has the severe drawback of requiring a great many iterations forfunctions which have long, narrow valley structures. In such cases, a Conjugate Gradient Method ispreferable.

References

Arfken, G. ``The Method of Steepest Descents.'' §7.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 428-436, 1985.

Menzel, D. (Ed.). Fundamental Formulas of Physics, Vol. 2, 2nd ed. New York: Dover, p. 80, 1960.

Morse, P. M. and Feshbach, H. ``Asymptotic Series; Method of Steepest Descent.'' §4.6 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 434-443, 1953.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 414, 1992.

• Kuratowski's Closure-Component Problem
• Kuratowski's Theorem
• Kurtosis
• Kähler Manifold
• König-Egeváry Theorem
• Königsberg Bridge Problem
• König's Theorem
• Kürschák's Tile
• L1-Norm
• L2-Norm
• L2-Space
• Labeled Graph
• Lacunarity
• Ladder
• Ladder Graph
• Lagrange Bracket
• Lagrange-Bürmann Theorem
• Lagrange Expansion
• Lagrange Interpolating Polynomial
• Lagrange Inversion Theorem
• Lagrange Multiplier
• Lagrange Number (Diophantine Equation)
• Lagrange Number (Rational Approximation)
• Lagrange Polynomial
• Lagrange Remainder