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Lloyd N. Trefethen
Lloyd Nicholas Trefethen (born 30 August 1955) is an American mathematician, professor of numerical analysis and head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford. Education Trefethen was born 30 August 1955 in Boston, Massachusetts, the son of mechanical engineer Lloyd M. Trefethen and codebreaker, poet, teacher and editor Florence Newman Trefethen. He obtained his bachelor's degree from Harvard University in 1977 and his master's from Stanford University in 1980. His PhD was on ''Wave Propagation and Stability for Finite Difference Schemes'' supervised by Joseph E. Oliger at Stanford University. Career and research Following his PhD, Trefethen went on to work at the Courant Institute of Mathematical Sciences in New York, Massachusetts Institute of Technology, and Cornell University, before being appointed to a chair at the University of Oxford and a Fellowship of Balliol College, Oxford. , he has published around 150 journal p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books by decree in 1586, it is the second oldest university press after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics known as the Delegates of the Press, who are appointed by the vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, opposite Somerville College, in the inner suburb of Jericho. For the last 500 years, OUP has primarily focused on the publication of pedagogical texts a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mark Embree
Mark Embree is professor of computational and applied mathematicsbr>at Virginia Tech in Blacksburg, Virginia. Until 2013, he was a professor of computational and applied mathematics at Rice University in Houston, Texas. Mark Embree was awarded Man of the Year and Outstanding Student in the College of Arts and Sciences at Virginia Tech in 1996. He was also a Rhodes Scholar at the University of Oxford, where he completed his doctorate. Early life Mark Embree attended Thomas Jefferson High School for Science and Technology. Research His main research interests are Krylov subspace methods, non-normal operators and spectral perturbation theory, Toeplitz matrices, random matrices, and damped wave operators. Books Dr Mark Embree wrote a book with Lloyd N. Trefethen titled Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators'' See also * Embree–Trefethen constant In mathematics, the random Fibonacci sequence is a stochastic analogue of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISI Highly Cited Researcher
The Institute for Scientific Information (ISI) was an academic publishing service, founded by Eugene Garfield in Philadelphia in 1956. ISI offered scientometric and bibliographic database services. Its specialty was citation indexing and analysis, a field pioneered by Garfield. Services ISI maintained citation databases covering thousands of academic journals, including a continuation of its longtime print-based indexing service the Science Citation Index (SCI), as well as the Social Sciences Citation Index (SSCI) and the Arts and Humanities Citation Index (AHCI). All of these were available via ISI's Web of Knowledge database service. This database allows a researcher to identify which articles have been cited most frequently, and who has cited them. The database provides some measure of the academic impact of the papers indexed in it, and may increase their impact by making them more visible and providing them with a quality label. Some anecdotal evidence suggests that appear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lasers
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow. A laser differs from other sources of light in that it emits light which is ''coherent''. Spatial coherence allows a laser to be focused to a tight spot, enabling applications such as laser cutting and lithography. Spatial coherence also allows a laser beam to stay narrow over great distances (collimation), enabling applications such as laser pointers and lidar (light detection and ranging). Lasers can also have high temporal coherence, which allows them to emit light with a very narrow spectrum. Alternatively, temporal coherence can be used to produce ultrashort pulses of light wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Matrix
In mathematics, a complex square matrix is normal if it commutes with its conjugate transpose : The concept of normal matrices can be extended to normal operators on infinite dimensional normed spaces and to normal elements in C*-algebras. As in the matrix case, normality means commutativity is preserved, to the extent possible, in the noncommutative setting. This makes normal operators, and normal elements of C*-algebras, more amenable to analysis. The spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix satisfying the equation is diagonalizable. The converse does not hold because diagonalizable matrices may have non-orthogonal eigenspaces. The left and right singular vectors in the singular value decomposition of a normal matrix \mathbf = \mathbf \boldsymbol \mathbf^* differ only in complex phase from each other and from the corresponding eigenvectors, since the phase must be factored ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudospectrum
In mathematics, the pseudospectrum of an operator is a set containing the spectrum of the operator and the numbers that are "almost" eigenvalues In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b .... Knowledge of the pseudospectrum can be particularly useful for understanding non-normal operators and their eigenfunctions. The ε-pseudospectrum of a matrix ''A'' consists of all eigenvalues of matrices which are ε-close to ''A'': :\Lambda_\epsilon(A) = \. Numerical algorithms which calculate the eigenvalues of a matrix give only approximate results due to rounding and other errors. These errors can be described with the matrix ''E''. More generally, for Banach spaces X,Y and operators A: X \to Y , one can define the \epsilon-pseudospectrum of A (typically denote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions). History Complex analysis is one of the classical branches in mathematics, with roots in the 18th century and just prior. Important mathematicians associated with comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a ''macroscopic'' viewpoint rather than from ''microscopic''. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Linear Algebra
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible. Numerical linear algebra aims to solve problems of continuous mathematics using finite precision computers, so its applications to the natural and social sciences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic roo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courant Institute Of Mathematical Sciences
The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research centers in the world. Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute and also a mathematics professor at New York University from 1936 to 1972, and serves as a center for research and advanced training in computer science and mathematics. It is located on Gould Plaza next to the New York University Stern School of Business, Stern School of Business and the economics department of the New York University College of Arts & Science, College of Arts and Science. NYU is ranked #1 in applied mathematics in the US (as per US News), #5 in citation impact worldwide, and #12 in citation worldwide. It is also ranked #19 worldwide in computer science and information systems. On the Faculty Scholarly Product ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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