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Eldon Robert Hansen
Eldon Robert Hansen is an American mathematician and author who has published in global optimization theory and interval arithmetic. Hansens's primary publications include ''Global Optimization Using Interval Analysis'' (1992), ''A Table of Series and Products'' (1975), and ''Topics in Interval Analysis'' (1969). He also co-authored a number of works with the mathematician William Walster. Background He was born in 1927 near Rochester, Washington. He completed his undergraduate studies at the University of California, Berkeley. Hansen received his Ph.D. in mathematics from Stanford University in 1960 on Jacobi methods and Block-Jacobi methods for computing matrix eigenvalues (Bulletin of the American Mathematical Society, 1961). Hansen taught at Stanford University, The University of California at Berkeley, San Jose State College, Oxford University, and Washington State University; Hansen also worked at Lockheed Corporation in Palo Alto, California. Research Hansen's al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval Arithmetic
Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation. Numerical methods using interval arithmetic can guarantee reliable and mathematically correct results. Instead of representing a value as a single number, interval arithmetic represents each value as a range of possibilities. For example, instead of saying the height of someone is approximately 2 meters, one could using interval arithmetic, say that the height of the person is definitely between 1.97 meters and 2.03 meters. Mathematically, using interval arithmetic, instead of working with an uncertain real-valued variable x, one works with an interval ,b/math> that defines the range of values that x can have. In other words, any value of the variable x lies in the closed interval between a and b. A function f, when applied to x, yields an inexact value; f ins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rochester, Washington
Rochester () is a census-designated place (CDP) in Thurston County, Washington, United States. It was founded in 1852, and the 2020 census recorded its population at 6,064. According to the United States Census Bureau, the CDP has a total area of 2.3 square miles (6.0 square kilometers), all of it land. Rochester Schools had 2,105 students registered in 2021-22 School Year. History Rochester was platted in 1890, and named after Rochester, Indiana, the native home of a first settler. An early variant name was "Key". Demographics As of the census of 2000, there were 1,829 people, 647 households, and 505 families residing in the CDP. The population density was 790.2 people per square mile (305.7/km2). There were 677 housing units at an average density of 292.5/sq mi (113.2/km2). The racial makeup of the CDP was 88.41% White, 0.16% African American, 1.69% Native American, 0.93% Asian, 0.11% Pacific Islander, 5.52% from other races, and 3.17% from two or more races. Hispanic or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant university and the founding campus of the University of California system. Its fourteen colleges and schools offer over 350 degree programs and enroll some 31,800 undergraduate and 13,200 graduate students. Berkeley ranks among the world's top universities. A founding member of the Association of American Universities, Berkeley hosts many leading research institutes dedicated to science, engineering, and mathematics. The university founded and maintains close relationships with three national laboratories at Berkeley, Livermore and Los Alamos, and has played a prominent role in many scientific advances, from the Manhattan Project and the discovery of 16 chemical elements to breakthroughs in computer science and genomics. Berkeley is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considered among the most prestigious universities in the world. Stanford was founded in 1885 by Leland and Jane Stanford in memory of their only child, Leland Stanford Jr., who had died of typhoid fever at age 15 the previous year. Leland Stanford was a U.S. senator and former governor of California who made his fortune as a railroad tycoon. The school admitted its first students on October 1, 1891, as a coeducational and non-denominational institution. Stanford University struggled financially after the death of Leland Stanford in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, provost of Stanford Frederick Terman inspired and supported faculty and graduates' entrepreneu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Method
In numerical linear algebra, the Jacobi 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. Description Let :A\mathbf x = \mathbf b be a square system of ''n'' linear equations, where: A = \begin a_ & a_ & \cdots & a_ \\ a_ & a_ & \cdots & a_ \\ \vdots & \vdots & \ddots & \vdots \\a_ & a_ & \cdots & a_ \end, \qquad \mathbf = \begin x_ \\ x_2 \\ \vdots \\ x_n \end , \qquad \mathbf = \begin b_ \\ b_2 \\ \vdots \\ b_n \end. Then ''A'' can be decomposed into a diagonal component ''D'', a lower triangular part ''L'' and an upper triangular part ''U'': :A=D+L+U \qquad \text \qquad D = \begin a_ & 0 & \cdots & 0 \\ 0 & a_ & \cdot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvalue Algorithm
In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Eigenvalues and eigenvectors Given an square matrix of real or complex numbers, an ''eigenvalue'' and its associated ''generalized eigenvector'' are a pair obeying the relation :\left(A - \lambda I\right)^k = 0, where is a nonzero column vector, is the identity matrix, is a positive integer, and both and are allowed to be complex even when is real. When , the vector is called simply an ''eigenvector'', and the pair is called an ''eigenpair''. In this case, . Any eigenvalue of has ordinaryThe term "ordinary" is used here only to emphasize the distinction between "eigenvector" and "generalized eigenvector". eigenvectors associated to it, for if is the smallest integer such that for a generalized eigenvector , then is an ordinary eigenvector. The value can always ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
San Jose State College
San José State University (San Jose State or SJSU) is a public university in San Jose, California. Established in 1857, SJSU is the oldest public university on the West Coast and the founding campus of the California State University (CSU) system. Located in downtown San Jose, the SJSU main campus is situated on , or roughly 19 square blocks. As of fall 2021, SJSU offers 143 bachelor's degree programs, 95 master's degrees, four doctoral degrees, 11 different credential programs and 38 certificates. SJSU is accredited by the WASC Senior College and University Commission. SJSU's total enrollment was 33,849 in fall 2021, including approximately 5,700 graduate and credential students. SJSU's student population is one of the most ethnically diverse in the nation. As of fall 2021, graduate student enrollment, Asian, and international student enrollments at SJSU were the highest of any campus in the CSU system. SJSU is consistently listed among the leading suppliers of undergradu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State University Of New York
The State University of New York (SUNY, , ) is a system of public colleges and universities in the State of New York. It is one of the largest comprehensive system of universities, colleges, and community colleges in the United States. Led by chancellor John B. King, the SUNY system has 91,182 employees, including 32,496 faculty members, and some 7,660 degree and certificate programs overall and a $13.08 billion budget. Its flagship universities are Stony Brook University and the University at Buffalo. SUNY's administrative offices are in Albany, the state's capital, with satellite offices in Manhattan and Washington, D.C. With 25,000 acres of land, SUNY's largest campus is SUNY College of Environmental Science and Forestry, which neighbors the State University of New York Upstate Medical University - the largest employer in the SUNY system with over 10,959 employees. The State University of New York was established in 1948 by Governor Thomas E. Dewey, through legislative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lockheed Corporation
The Lockheed Corporation was an American aerospace manufacturer. Lockheed was founded in 1926 and later merged with Martin Marietta to form Lockheed Martin in 1995. Its founder, Allan Lockheed, had earlier founded the similarly named but otherwise-unrelated Loughead Aircraft Manufacturing Company, which was operational from 1912 to 1920. History Origins Allan Loughead and his brother Malcolm Loughead had operated an earlier aircraft company, Loughead Aircraft Manufacturing Company, which was operational from 1912 to 1920. The company built and operated aircraft for paying passengers on sightseeing tours in California and had developed a prototype for the civil market, but folded in 1920 due to the flood of surplus aircraft deflating the market after World War I. Allan went into the real estate market while Malcolm had meanwhile formed a successful company marketing brake systems for automobiles. On December 13, 1926, Allan Lockheed, Jack Northrop, John Northrop, Kenneth K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palo Alto, California
Palo Alto (; Spanish language, Spanish for "tall stick") is a charter city in the northwestern corner of Santa Clara County, California, United States, in the San Francisco Bay Area, named after a Sequoia sempervirens, coastal redwood tree known as El Palo Alto. The city was established in 1894 by the American industrialist Leland Stanford when he founded Stanford University in memory of his son, Leland Stanford Jr. Palo Alto includes portions of Stanford University and borders East Palo Alto, California, East Palo Alto, Mountain View, California, Mountain View, Los Altos, California, Los Altos, Los Altos Hills, California, Los Altos Hills, Stanford, California, Stanford, Portola Valley, California, Portola Valley, and Menlo Park, California, Menlo Park. At the 2010 United States Census, 2020 census, the population was 68,572. Palo Alto is one of the most expensive cities in the United States in which to live, and its residents are among the most educated in the country. Howeve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss–Seidel Method
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobi method. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either strictly diagonally dominant, or symmetric and positive definite. It was only mentioned in a private letter from Gauss to his student Gerling in 1823. A publication was not delivered before 1874 by Seidel. Description The Gauss–Seidel method is an iterative technique for solving a square system of linear equations with unknown : A\mathbf x = \mathbf b . It is defined by the iteration L_* \mathbf^ = \mathbf - U \mathbf^, where \mathbf^ is the -th approximation or iteration of \mathbf,\,\mathbf^ is the next or -th it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval Computation
Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation. Numerical methods using interval arithmetic can guarantee reliable and mathematically correct results. Instead of representing a value as a single number, interval arithmetic represents each value as a range of possibilities. For example, instead of saying the height of someone is approximately 2 meters, one could using interval arithmetic, say that the height of the person is definitely between 1.97 meters and 2.03 meters. Mathematically, using interval arithmetic, instead of working with an uncertain real-valued variable x, one works with an interval ,b/math> that defines the range of values that x can have. In other words, any value of the variable x lies in the closed interval between a and b. A function f, when applied to x, yields an inexact value; f in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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