Matrices, moments, and quadrature with applications /:
This computationally oriented work describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, N.J. ; Oxford :
Princeton University Press,
[2010]
|
| Series: | Princeton series in applied mathematics.
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | This computationally oriented work describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. |
| Physical Description: | 1 online resource (ix, 363 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 335-359) and index. |
| ISBN: | 9781400833887 1400833884 1282458019 9781282458017 |
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MARC
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| 100 | 1 | |a Golub, Gene H. |q (Gene Howard), |d 1932-2007. |1 https://id.oclc.org/worldcat/entity/E39PBJt8gwHDdkpyjk6CccPxXd |0 http://id.loc.gov/authorities/names/n83005601 | |
| 245 | 1 | 0 | |a Matrices, moments, and quadrature with applications / |c Gene H. Golub and Gérard Meurant. |
| 264 | 1 | |a Princeton, N.J. ; |a Oxford : |b Princeton University Press, |c [2010] | |
| 264 | 4 | |c ©2010 | |
| 300 | |a 1 online resource (ix, 363 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Princeton series in applied mathematics | |
| 504 | |a Includes bibliographical references (pages 335-359) and index. | ||
| 520 | 8 | |a This computationally oriented work describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preliminaries; Contents; Preface; Chapter 1. Introduction; Chapter 2. Orthogonal Polynomials; Chapter 3. Properties of Tridiagonal Matrices; Chapter 4. The Lanczos and Conjugate Gradient Algorithms; Chapter 5. Computation of the Jacobi Matrices; Chapter 6. Gauss Quadrature; Chapter 7. Bounds for Bilinear Forms uT f(A)v; Chapter 8. Extensions to Nonsymmetric Matrices; Chapter 9. Solving Secular Equations; Chapter 10. Examples of Gauss Quadrature Rules; Chapter 11. Bounds and Estimates for Elements of Functions of Matrices. | |
| 650 | 0 | |a Matrices. |0 http://id.loc.gov/authorities/subjects/sh85082210 | |
| 650 | 0 | |a Numerical analysis. |0 http://id.loc.gov/authorities/subjects/sh85093237 | |
| 650 | 6 | |a Matrices. | |
| 650 | 6 | |a Analyse numérique. | |
| 650 | 7 | |a MATHEMATICS |x Matrices. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 7 | |a Matrices |2 fast | |
| 650 | 7 | |a Numerical analysis |2 fast | |
| 650 | 7 | |a Algorithmus |2 gnd |0 http://d-nb.info/gnd/4001183-5 | |
| 650 | 7 | |a Bilinearform |2 gnd |0 http://d-nb.info/gnd/4138018-6 | |
| 650 | 7 | |a Matrix |g Mathematik |2 gnd |0 http://d-nb.info/gnd/4037968-1 | |
| 650 | 7 | |a Numerisches Verfahren |2 gnd |0 http://d-nb.info/gnd/4128130-5 | |
| 650 | 7 | |a Orthogonale Polynome |2 gnd | |
| 650 | 7 | |a Matrix |x (Math.) |x Numerische Mathematik. |2 idsbb | |
| 650 | 7 | |a Numerische Mathematik |x Matrix (Math.) |2 idsbb | |
| 653 | |a Algorithm. | ||
| 653 | |a Analysis of algorithms. | ||
| 653 | |a Analytic function. | ||
| 653 | |a Asymptotic analysis. | ||
| 653 | |a Basis (linear algebra). | ||
| 653 | |a Basis function. | ||
| 653 | |a Biconjugate gradient method. | ||
| 653 | |a Bidiagonal matrix. | ||
| 653 | |a Bilinear form. | ||
| 653 | |a Calculation. | ||
| 653 | |a Characteristic polynomial. | ||
| 653 | |a Chebyshev polynomials. | ||
| 653 | |a Coefficient. | ||
| 653 | |a Complex number. | ||
| 653 | |a Computation. | ||
| 653 | |a Condition number. | ||
| 653 | |a Conjugate gradient method. | ||
| 653 | |a Conjugate transpose. | ||
| 653 | |a Cross-validation (statistics). | ||
| 653 | |a Curve fitting. | ||
| 653 | |a Degeneracy (mathematics). | ||
| 653 | |a Determinant. | ||
| 653 | |a Diagonal matrix. | ||
| 653 | |a Dimension (vector space). | ||
| 653 | |a Eigenvalues and eigenvectors. | ||
| 653 | |a Equation. | ||
| 653 | |a Estimation. | ||
| 653 | |a Estimator. | ||
| 653 | |a Exponential function. | ||
| 653 | |a Factorization. | ||
| 653 | |a Function (mathematics). | ||
| 653 | |a Function of a real variable. | ||
| 653 | |a Functional analysis. | ||
| 653 | |a Gaussian quadrature. | ||
| 653 | |a Hankel matrix. | ||
| 653 | |a Hermite interpolation. | ||
| 653 | |a Hessenberg matrix. | ||
| 653 | |a Hilbert matrix. | ||
| 653 | |a Holomorphic function. | ||
| 653 | |a Identity matrix. | ||
| 653 | |a Interlacing (bitmaps). | ||
| 653 | |a Inverse iteration. | ||
| 653 | |a Inverse problem. | ||
| 653 | |a Invertible matrix. | ||
| 653 | |a Iteration. | ||
| 653 | |a Iterative method. | ||
| 653 | |a Jacobi matrix. | ||
| 653 | |a Krylov subspace. | ||
| 653 | |a Laguerre polynomials. | ||
| 653 | |a Lanczos algorithm. | ||
| 653 | |a Linear differential equation. | ||
| 653 | |a Linear regression. | ||
| 653 | |a Linear subspace. | ||
| 653 | |a Logarithm. | ||
| 653 | |a Machine epsilon. | ||
| 653 | |a Matrix function. | ||
| 653 | |a Matrix polynomial. | ||
| 653 | |a Maxima and minima. | ||
| 653 | |a Mean value theorem. | ||
| 653 | |a Meromorphic function. | ||
| 653 | |a Moment (mathematics). | ||
| 653 | |a Moment matrix. | ||
| 653 | |a Moment problem. | ||
| 653 | |a Monic polynomial. | ||
| 653 | |a Monomial. | ||
| 653 | |a Monotonic function. | ||
| 653 | |a Newton's method. | ||
| 653 | |a Numerical analysis. | ||
| 653 | |a Numerical integration. | ||
| 653 | |a Numerical linear algebra. | ||
| 653 | |a Orthogonal basis. | ||
| 653 | |a Orthogonal matrix. | ||
| 653 | |a Orthogonal polynomials. | ||
| 653 | |a Orthogonal transformation. | ||
| 653 | |a Orthogonality. | ||
| 653 | |a Orthogonalization. | ||
| 653 | |a Orthonormal basis. | ||
| 653 | |a Partial fraction decomposition. | ||
| 653 | |a Polynomial. | ||
| 653 | |a Preconditioner. | ||
| 653 | |a QR algorithm. | ||
| 653 | |a QR decomposition. | ||
| 653 | |a Quadratic form. | ||
| 653 | |a Rate of convergence. | ||
| 653 | |a Recurrence relation. | ||
| 653 | |a Regularization (mathematics). | ||
| 653 | |a Rotation matrix. | ||
| 653 | |a Singular value. | ||
| 653 | |a Square (algebra). | ||
| 653 | |a Summation. | ||
| 653 | |a Symmetric matrix. | ||
| 653 | |a Theorem. | ||
| 653 | |a Tikhonov regularization. | ||
| 653 | |a Trace (linear algebra). | ||
| 653 | |a Triangular matrix. | ||
| 653 | |a Tridiagonal matrix. | ||
| 653 | |a Upper and lower bounds. | ||
| 653 | |a Variable (mathematics). | ||
| 653 | |a Vector space. | ||
| 653 | |a Weight function. | ||
| 700 | 1 | |a Meurant, Gérard A. | |
| 758 | |i has work: |a Matrices, moments, and quadrature with applications (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGbfcbtjwCC8q7qyHJPG73 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Golub, Gene H. (Gene Howard), 1932-2007. |t Matrices, moments, and quadrature with applications. |d Princeton, N.J. ; Oxford : Princeton University Press, ©2010 |z 9780691143415 |w (OCoLC)461270987 |
| 830 | 0 | |a Princeton series in applied mathematics. |0 http://id.loc.gov/authorities/names/no2002046464 | |
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Record in the Search Index
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| _version_ | 1829094687854559232 |
| adam_text | |
| any_adam_object | |
| author | Golub, Gene H. (Gene Howard), 1932-2007 |
| author2 | Meurant, Gérard A. |
| author2_role | |
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| author_GND | http://id.loc.gov/authorities/names/n83005601 |
| author_facet | Golub, Gene H. (Gene Howard), 1932-2007 Meurant, Gérard A. |
| author_role | |
| author_sort | Golub, Gene H. 1932-2007 |
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| contents | Preliminaries; Contents; Preface; Chapter 1. Introduction; Chapter 2. Orthogonal Polynomials; Chapter 3. Properties of Tridiagonal Matrices; Chapter 4. The Lanczos and Conjugate Gradient Algorithms; Chapter 5. Computation of the Jacobi Matrices; Chapter 6. Gauss Quadrature; Chapter 7. Bounds for Bilinear Forms uT f(A)v; Chapter 8. Extensions to Nonsymmetric Matrices; Chapter 9. Solving Secular Equations; Chapter 10. Examples of Gauss Quadrature Rules; Chapter 11. Bounds and Estimates for Elements of Functions of Matrices. |
| ctrlnum | (OCoLC)697182001 |
| dewey-full | 512.9434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9434 |
| dewey-search | 512.9434 |
| dewey-sort | 3512.9434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn697182001 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:37:06Z |
| institution | BVB |
| isbn | 9781400833887 1400833884 1282458019 9781282458017 |
| language | English |
| oclc_num | 697182001 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (ix, 363 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Princeton University Press, |
| record_format | marc |
| series | Princeton series in applied mathematics. |
| series2 | Princeton series in applied mathematics |
| spelling | Golub, Gene H. (Gene Howard), 1932-2007. https://id.oclc.org/worldcat/entity/E39PBJt8gwHDdkpyjk6CccPxXd http://id.loc.gov/authorities/names/n83005601 Matrices, moments, and quadrature with applications / Gene H. Golub and Gérard Meurant. Princeton, N.J. ; Oxford : Princeton University Press, [2010] ©2010 1 online resource (ix, 363 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Princeton series in applied mathematics Includes bibliographical references (pages 335-359) and index. This computationally oriented work describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. Print version record. Preliminaries; Contents; Preface; Chapter 1. Introduction; Chapter 2. Orthogonal Polynomials; Chapter 3. Properties of Tridiagonal Matrices; Chapter 4. The Lanczos and Conjugate Gradient Algorithms; Chapter 5. Computation of the Jacobi Matrices; Chapter 6. Gauss Quadrature; Chapter 7. Bounds for Bilinear Forms uT f(A)v; Chapter 8. Extensions to Nonsymmetric Matrices; Chapter 9. Solving Secular Equations; Chapter 10. Examples of Gauss Quadrature Rules; Chapter 11. Bounds and Estimates for Elements of Functions of Matrices. Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Matrices. Analyse numérique. MATHEMATICS Matrices. bisacsh MATHEMATICS Applied. bisacsh Matrices fast Numerical analysis fast Algorithmus gnd http://d-nb.info/gnd/4001183-5 Bilinearform gnd http://d-nb.info/gnd/4138018-6 Matrix Mathematik gnd http://d-nb.info/gnd/4037968-1 Numerisches Verfahren gnd http://d-nb.info/gnd/4128130-5 Orthogonale Polynome gnd Matrix (Math.) Numerische Mathematik. idsbb Numerische Mathematik Matrix (Math.) idsbb Algorithm. Analysis of algorithms. Analytic function. Asymptotic analysis. Basis (linear algebra). Basis function. Biconjugate gradient method. Bidiagonal matrix. Bilinear form. Calculation. Characteristic polynomial. Chebyshev polynomials. Coefficient. Complex number. Computation. Condition number. Conjugate gradient method. Conjugate transpose. Cross-validation (statistics). Curve fitting. Degeneracy (mathematics). Determinant. Diagonal matrix. Dimension (vector space). Eigenvalues and eigenvectors. Equation. Estimation. Estimator. Exponential function. Factorization. Function (mathematics). Function of a real variable. Functional analysis. Gaussian quadrature. Hankel matrix. Hermite interpolation. Hessenberg matrix. Hilbert matrix. Holomorphic function. Identity matrix. Interlacing (bitmaps). Inverse iteration. Inverse problem. Invertible matrix. Iteration. Iterative method. Jacobi matrix. Krylov subspace. Laguerre polynomials. Lanczos algorithm. Linear differential equation. Linear regression. Linear subspace. Logarithm. Machine epsilon. Matrix function. Matrix polynomial. Maxima and minima. Mean value theorem. Meromorphic function. Moment (mathematics). Moment matrix. Moment problem. Monic polynomial. Monomial. Monotonic function. Newton's method. Numerical analysis. Numerical integration. Numerical linear algebra. Orthogonal basis. Orthogonal matrix. Orthogonal polynomials. Orthogonal transformation. Orthogonality. Orthogonalization. Orthonormal basis. Partial fraction decomposition. Polynomial. Preconditioner. QR algorithm. QR decomposition. Quadratic form. Rate of convergence. Recurrence relation. Regularization (mathematics). Rotation matrix. Singular value. Square (algebra). Summation. Symmetric matrix. Theorem. Tikhonov regularization. Trace (linear algebra). Triangular matrix. Tridiagonal matrix. Upper and lower bounds. Variable (mathematics). Vector space. Weight function. Meurant, Gérard A. has work: Matrices, moments, and quadrature with applications (Text) https://id.oclc.org/worldcat/entity/E39PCGbfcbtjwCC8q7qyHJPG73 https://id.oclc.org/worldcat/ontology/hasWork Print version: Golub, Gene H. (Gene Howard), 1932-2007. Matrices, moments, and quadrature with applications. Princeton, N.J. ; Oxford : Princeton University Press, ©2010 9780691143415 (OCoLC)461270987 Princeton series in applied mathematics. http://id.loc.gov/authorities/names/no2002046464 |
| spellingShingle | Golub, Gene H. (Gene Howard), 1932-2007 Matrices, moments, and quadrature with applications / Princeton series in applied mathematics. Preliminaries; Contents; Preface; Chapter 1. Introduction; Chapter 2. Orthogonal Polynomials; Chapter 3. Properties of Tridiagonal Matrices; Chapter 4. The Lanczos and Conjugate Gradient Algorithms; Chapter 5. Computation of the Jacobi Matrices; Chapter 6. Gauss Quadrature; Chapter 7. Bounds for Bilinear Forms uT f(A)v; Chapter 8. Extensions to Nonsymmetric Matrices; Chapter 9. Solving Secular Equations; Chapter 10. Examples of Gauss Quadrature Rules; Chapter 11. Bounds and Estimates for Elements of Functions of Matrices. Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Matrices. Analyse numérique. MATHEMATICS Matrices. bisacsh MATHEMATICS Applied. bisacsh Matrices fast Numerical analysis fast Algorithmus gnd http://d-nb.info/gnd/4001183-5 Bilinearform gnd http://d-nb.info/gnd/4138018-6 Matrix Mathematik gnd http://d-nb.info/gnd/4037968-1 Numerisches Verfahren gnd http://d-nb.info/gnd/4128130-5 Orthogonale Polynome gnd Matrix (Math.) Numerische Mathematik. idsbb Numerische Mathematik Matrix (Math.) idsbb |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082210 http://id.loc.gov/authorities/subjects/sh85093237 http://d-nb.info/gnd/4001183-5 http://d-nb.info/gnd/4138018-6 http://d-nb.info/gnd/4037968-1 http://d-nb.info/gnd/4128130-5 |
| title | Matrices, moments, and quadrature with applications / |
| title_auth | Matrices, moments, and quadrature with applications / |
| title_exact_search | Matrices, moments, and quadrature with applications / |
| title_full | Matrices, moments, and quadrature with applications / Gene H. Golub and Gérard Meurant. |
| title_fullStr | Matrices, moments, and quadrature with applications / Gene H. Golub and Gérard Meurant. |
| title_full_unstemmed | Matrices, moments, and quadrature with applications / Gene H. Golub and Gérard Meurant. |
| title_short | Matrices, moments, and quadrature with applications / |
| title_sort | matrices moments and quadrature with applications |
| topic | Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Matrices. Analyse numérique. MATHEMATICS Matrices. bisacsh MATHEMATICS Applied. bisacsh Matrices fast Numerical analysis fast Algorithmus gnd http://d-nb.info/gnd/4001183-5 Bilinearform gnd http://d-nb.info/gnd/4138018-6 Matrix Mathematik gnd http://d-nb.info/gnd/4037968-1 Numerisches Verfahren gnd http://d-nb.info/gnd/4128130-5 Orthogonale Polynome gnd Matrix (Math.) Numerische Mathematik. idsbb Numerische Mathematik Matrix (Math.) idsbb |
| topic_facet | Matrices. Numerical analysis. Analyse numérique. MATHEMATICS Matrices. MATHEMATICS Applied. Matrices Numerical analysis Algorithmus Bilinearform Matrix Mathematik Numerisches Verfahren Orthogonale Polynome Matrix (Math.) Numerische Mathematik. Numerische Mathematik Matrix (Math.) |
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