InterpolationIn the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.
Bilinear interpolationIn mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in another direction.
Trigonometric interpolationIn mathematics, trigonometric interpolation is interpolation with trigonometric polynomials. Interpolation is the process of finding a function which goes through some given data points. For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and cosines of given periods. This form is especially suited for interpolation of periodic functions. An important special case is when the given data points are equally spaced, in which case the solution is given by the discrete Fourier transform.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Multivariate interpolationIn numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points . Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).
Polynomial interpolationIn numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.
Gaussian quadratureIn numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. (See numerical integration for more on quadrature rules.) An n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree 2n − 1 or less by a suitable choice of the nodes x_i and weights w_i for i = 1, ..., n.
Nearest-neighbor interpolationNearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
House of BourbonThe House of Bourbon (ˈbʊərbən, also UKˈbɔrbɒn; buʁbɔ̃) is a dynasty that originated in the Kingdom of France and is a branch of the Capetian dynasty, the royal House of France. Bourbon kings first ruled France and Navarre in the 16th century, and by the 18th century, members of the Spanish Bourbon dynasty held thrones in Spain, Naples, Sicily, and Parma. Today Spain and Luxembourg have monarchs of the House of Bourbon. The royal Bourbons originated in 1272, when Robert, the youngest son of King Louis IX of France, married the heiress of the lordship of Bourbon.
Notebook for Anna Magdalena BachThe title Notebook for Anna Magdalena Bach (Notenbüchlein für Anna Magdalena Bach) refers to either of two manuscript notebooks that the German Baroque composer Johann Sebastian Bach presented to his second wife, Anna Magdalena. Keyboard music (minuets, rondeaux, polonaises, chorales, sonatas, preludes, musettes, marches, gavottes) makes up most of both notebooks, and a few pieces for voice (songs, and arias) are included. The Notebooks provide a glimpse into the domestic music of the 18th century and the musical tastes of the Bach family.
Alfred and EmilyAlfred and Emily is a book by Doris Lessing in a new hybrid form. Part fiction, part notebook, part memoir, it was first published in 2008. The book is based on the lives of Lessing's parents. Part one is a novella, a fictional portrait of how her parents' lives might have been without the interruption of the First World War. Part two is a retelling of how her parents' lives really developed. The novella begins in England in 1902, when Alfred and Emily meet at a cricket match.
Jean-Claude Van DammeJean-Claude Camille François Van Varenberg (ʒɑ̃ klod kamij fʁɑ̃swa vɑ̃ vaʁɑ̃bɛʁɡ; vɑn ˈvarə(n)ˈbɛrx; born 18 October 1960), known professionally as Jean-Claude Van Damme (vɑ̃ dam; vɑn ˈdɑmə), is a Belgian martial artist, actor, filmmaker, and fight choreographer. Born and raised in Brussels, Belgium, at the age of ten his father enrolled him in a Shotokan school. Starting in the late 1970s, Van Damme competed in several semi-contact and full-contact matches in both karate and kickboxing.
Tom Friedman (artist)Tom Friedman (born 1965) is an American conceptual sculptor. He was born in St. Louis, Missouri and received a BFA in graphic illustration from Washington University in St. Louis (1988) and an MFA in sculpture from the University of Illinois at Chicago (1990.). As a conceptual artist he works in diverse media including sculpture, painting, drawing, video, and installation. For over twenty years, Friedman has been investigating the viewer/object relationship, and "the space in between.
Fritz the CatFritz the Cat is a comic strip created by Robert Crumb. Set in a "supercity" of anthropomorphic animals, it focused on Fritz, a tabby cat who frequently went on wild adventures that sometimes involved sexual escapades. Crumb began drawing the character in homemade comic books as a child. Fritz became one of his best-known characters, thanks largely to the motion picture adaptation by Ralph Bakshi.
Frank PiatekFrank Piatek (born 1944) is an American artist, known for abstract, illusionistic paintings of tubular forms and three-dimensional works exploring spirituality, cultural memory and the creative process. Piatek emerged in the mid-1960s, among a group of Chicago artists exploring various types of organic abstraction that shared qualities with the Chicago Imagists; his work, however relies more on suggestion than expressionistic representation.
Nicolás Cámara ValesNicolás Cámara Vales (1875 — 1956) was a Mexican liberal politician, diplomat and physician who served as governor of Yucatán on two occasions between 1911 and 1913 during the Mexican Revolution. After graduating from the University of Berlin as a Doctor of Medicine, he returned to Mérida where he specialized in pediatrics, opening the first children's hospital in the Yucatán Peninsula. After 1909, he joined José María Pino Suárez, his brother-in-law, campaigning in favor of Francisco I. Madero who wanted to democratize Mexico.
Finite difference methodIn numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
École Polytechnique Fédérale de LausanneThe École polytechnique fédérale de Lausanne (EPFL; English: Swiss Federal Institute of Technology in Lausanne; Eidgenössische Technische Hochschule Lausanne) is a public research university in Lausanne, Switzerland. Established in 1853, EPFL has placed itself as a university specializing in engineering and natural sciences. EPFL is part of the ETH Domain, which is directly dependent on the Federal Department of Economic Affairs, Education and Research.
My Father's Glory (film)My Father's Glory (original title: La Gloire de mon père) is a 1990 French film directed by Yves Robert, based on the autobiographical novel My Father's Glory by Marcel Pagnol. The sequel, which was also filmed by Robert in 1990, is My Mother's Castle (Le Château de ma mère). Both films are based on the cycle Souvenirs d'enfance, published in 1957. This film is set between 1900 and the First World War. Young Marcel was born in the country but raised in Marseilles. His father, Joseph, is a hard-working, atheistic school teacher in Marseilles.
