Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
ColumnA column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. The term column applies especially to a large round support (the shaft of the column) with a capital and a base or pedestal, which is made of stone, or appearing to be so. A small wooden or metal support is typically called a post.
Finite differenceA finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted is the operator that maps a function f to the function defined by A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives.
Solomonic columnThe Solomonic column, also called Barley-sugar column, is a helical column, characterized by a spiraling twisting shaft like a corkscrew. It is not associated with a specific classical order, although most examples have Corinthian or Composite capitals. But it may be crowned with any design, for example, making a Roman Doric solomonic or Ionic solomonic column.
Divided differencesIn mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation. Divided differences is a recursive division process. Given a sequence of data points , the method calculates the coefficients of the interpolation polynomial of these points in the Newton form.
Root-finding algorithmsIn mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f, from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number x such that f(x) = 0. As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form, root-finding algorithms provide approximations to zeros, expressed either as floating-point numbers or as small isolating intervals, or disks for complex roots (an interval or disk output being equivalent to an approximate output together with an error bound).
EntasisIn architecture, entasis is the application of a convex curve to a surface for aesthetic purposes. Its best-known use is in certain orders of Classical columns that curve slightly as their diameter is decreased from the bottom upward. It also may serve an engineering function regarding strength. The word we apply to the design principle is used by the Roman architectural historian Vitruvius, and derives from the Greek word έντείνω (enteino), "to stretch or strain tight".
CellaA cella (from Latin for small chamber) or naos (from the Greek ναός, "temple") is the inner chamber of an ancient Greek or Roman temple in classical antiquity. Its enclosure within walls has given rise to extended meanings, of a hermit's or monk's cell, and since the 17th century, of a biological cell in plants or animals. In ancient Greek and Roman temples the cella was a room at the center of the building, usually containing a or statue representing the particular deity venerated in the temple.
Ionic orderThe Ionic order is one of the three canonic orders of classical architecture, the other two being the Doric and the Corinthian. There are two lesser orders: the Tuscan (a plainer Doric), and the rich variant of Corinthian called the composite order. Of the three classical canonic orders, the Corinthian order has the narrowest columns, followed by the Ionic order, with the Doric order having the widest columns. The Ionic capital is characterized by the use of volutes.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
