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Stefano De Marchi
Stefano De Marchi (born 17 December 1962 in Candiana, Padua) is an Italian mathematician who works in numerical analysis and is a professor at the University of Padua. He is managing editor of the open access journal Dolomites Research Notes on Approximation published by the Padua University Press, coordinator of the Constructive Approximation and Applications Research Group, coordinator of the Research Italian network on Approximation, and responsible for the Unione Matematica Italiana Thematic Group on "Approximation Theory and Applications (A.T.A.)". His scientific interests deal mainly with interpolation and approximation of functions and data by polynomials and radial basis functions (RBFs)). Education and career Stefano De Marchi studied Bachelor's degree of Mathematics in 1981-1987, Master in Applied Mathematics in 1991 at the University of Padua, and received his doctorate in Computational Mathematics, Consorzio Nord-Orgientale, VI ciclo, University of Padua under Maria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Candiana
Candiana is a ''comune'' (municipality) in the Province of Padua in the Italian region Veneto, located about southwest of Venice and about southeast of Padua. As of 31 December 2004, it had a population of 2,468 and an area of .All demographics and other statistics: Italian statistical institute Istat. The municipality of Candiana contains the ''frazione A ''frazione'' (: ''frazioni'') is a type of subdivision of a ''comune'' ('municipality') in Italy, often a small village or hamlet outside the main town. Most ''frazioni'' were created during the Fascist era (1922–1943) as a way to consolidat ...'' (subdivision) Pontecasale. Candiana borders the following municipalities: Agna, Arre, Bovolenta, Correzzola, Pontelongo, Terrassa Padovana. Demographic evolution Colors= id:lightgrey value:gray(0.9) id:darkgrey value:gray(0.8) id:sfondo value:rgb(1,1,1) id:barra value:rgb(0.6,0.7,0.8) ImageSize = width:455 height:303 PlotArea = left:50 bottom:50 top:30 rig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Padua
Padua ( ) is a city and ''comune'' (municipality) in Veneto, northern Italy, and the capital of the province of Padua. The city lies on the banks of the river Bacchiglione, west of Venice and southeast of Vicenza, and has a population of 207,694 as of 2025. It is also the economic and communications hub of the area. Padua is sometimes included, with Venice and Treviso, in the Padua-Treviso-Venice Metropolitan Area (PATREVE) which has a population of around 2,600,000. Besides the Bacchiglione, the Brenta River, which once ran through the city, still touches the northern districts. Its agricultural setting is the Venetian Plain. To the city's south west lies the Euganean Hills, Euganaean Hills, which feature in poems by Lucan, Martial, Petrarch, Ugo Foscolo, and Percy Bysshe Shelley. Padua has two UNESCO World Heritage List entries: its Botanical Garden of Padua, Botanical Garden, which is the world's oldest, and its 14th-century frescoes, situated in Padua's fourteenth-centu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Padua
The University of Padua (, UNIPD) is an Italian public research university in Padua, Italy. It was founded in 1222 by a group of students and teachers from the University of Bologna, who previously settled in Vicenza; thus, it is the second-oldest university in Italy, as well as the world's fifth-oldest surviving university. The University of Padua was one of the most prominent universities in early modern Europe, known particularly for the rigor of its Aristotelian logic and science. Together with the University of Bologna, Padua had a central role in the Italian Renaissance, housing and educating a number of Italian Renaissance mathematicians, amongst them Nicolaus Copernicus. , it is made up of 32 departments and eight schools. Padua is part a network of historical research universities known as the Coimbra Group. In 2021, the university had approximately 72,000 students including undergraduates, postgraduates, and doctoral students. History The university is conventionally s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Theory
In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characterizing the approximation error, errors introduced thereby. What is meant by ''best'' and ''simpler'' will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials. One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or Rational function, rational (ratio of polynomials) approximations. The objective is to make the approxi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpolation
In the mathematics, 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 (statistics), sampling or experimentation, which represent the values of a function for a limited number of values of the Dependent and independent variables, independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable. A closely related problem is the function approximation, approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation
An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ''ad-'' (''ad-'' before ''p'' becomes ap- by assimilation) meaning ''to''. Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning. It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. In science, approximation can refer to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Basis Function
In mathematics a radial basis function (RBF) is a real-valued function \varphi whose value depends only on the distance between the input and some fixed point, either the origin, so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ), or some other fixed point \mathbf, called a ''center'', so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf-\mathbf\right\, ). Any function \varphi that satisfies the property \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ) is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection \_k which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Low ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the profession, professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of Mathematical analysis, applied analysis, most notably differential equations; approximation theory (broadly construed, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tullio Levi-Civita
Tullio Levi-Civita, (; ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus ( tensor calculus) and its applications to the theory of relativity, but who also made significant contributions in other areas. He was a pupil of Gregorio Ricci-Curbastro, the inventor of tensor calculus. His work included foundational papers in both pure and applied mathematics, celestial mechanics (notably on the three-body problem), analytic mechanics (the Levi-Civita separability conditions in the Hamilton–Jacobi equation) and hydrodynamics. Biography Born into an Italian Jewish family in Padua, Levi-Civita was the son of Giacomo Levi-Civita, a lawyer and former senator. He graduated in 1892 from the University of Padua Faculty of Mathematics. In 1894 he earned a teaching diploma after which he was appointed to the Faculty of Science teacher's college in Pavia. In 1898 he was appointed to the Padua Chair of Rational Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Padua Points
In polynomial interpolation of two variables, the Padua points are the first known example (and up to now the only one) of a unisolvent point set (that is, the interpolating polynomial is unique) with ''minimal growth'' of their Lebesgue constant, proven to be O(\log^2 n). Their name is due to the University of Padua, where they were originally discovered. The points are defined in the domain 1,1\times 1,1\subset \mathbb^2. It is possible to use the points with four orientations, obtained with subsequent 90-degree rotations: this way we get four different families of Padua points. The four families We can see the Padua point as a " sampling" of a parametric curve, called ''generating curve'', which is slightly different for each of the four families, so that the points for interpolation degree n and family s can be defined as :\text_n^s=\lbrace\mathbf=(\xi_1,\xi_2)\rbrace=\left\lbrace\gamma_s\left(\frac\right),k=0,\ldots,n(n+1)\right\rbrace. Actually, the Padua points l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
