The linear equations problem:
The simplest case of a linear equations problem is that of finding m unknowns by solving m linear algebraic non-homogeneous equations with given coefficients and constant terms. If this solution is carried out m times with the columns of the identity matrix as successive choices for the constant vec...
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Stanford, California
1959
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| Series: | Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report
3 |
| Subjects: | |
| Summary: | The simplest case of a linear equations problem is that of finding m unknowns by solving m linear algebraic non-homogeneous equations with given coefficients and constant terms. If this solution is carried out m times with the columns of the identity matrix as successive choices for the constant vector, the resulting sets of solutions form the columns of the inverse of the matrix coefficients. Another situation which is disposed of very simply in a purely theoretical treatment but which is non-trivial in practice is that in which there are more equations than unknowns, yet a solution is known, or at least believed, to exist. The purpose of the present paper is to describe a method of solving in a routine way a class of linear algebraic problems which include the various special cases mentioned. |
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| 520 | 3 | |a The simplest case of a linear equations problem is that of finding m unknowns by solving m linear algebraic non-homogeneous equations with given coefficients and constant terms. If this solution is carried out m times with the columns of the identity matrix as successive choices for the constant vector, the resulting sets of solutions form the columns of the inverse of the matrix coefficients. Another situation which is disposed of very simply in a purely theoretical treatment but which is non-trivial in practice is that in which there are more equations than unknowns, yet a solution is known, or at least believed, to exist. The purpose of the present paper is to describe a method of solving in a routine way a class of linear algebraic problems which include the various special cases mentioned. | |
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| id | DE-604.BV009930817 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:43:25Z |
| institution | BVB |
| language | English |
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| oclc_num | 227460639 |
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| owner_facet | DE-91G DE-BY-TUM |
| publishDate | 1959 |
| publishDateSearch | 1959 |
| publishDateSort | 1959 |
| record_format | marc |
| series | Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report |
| series2 | Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report |
| spelling | Givens, Wallace Verfasser aut The linear equations problem Stanford, California 1959 txt rdacontent n rdamedia nc rdacarrier Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report 3 The simplest case of a linear equations problem is that of finding m unknowns by solving m linear algebraic non-homogeneous equations with given coefficients and constant terms. If this solution is carried out m times with the columns of the identity matrix as successive choices for the constant vector, the resulting sets of solutions form the columns of the inverse of the matrix coefficients. Another situation which is disposed of very simply in a purely theoretical treatment but which is non-trivial in practice is that in which there are more equations than unknowns, yet a solution is known, or at least believed, to exist. The purpose of the present paper is to describe a method of solving in a routine way a class of linear algebraic problems which include the various special cases mentioned. (Equations dtict Algorithms dtict Determinants(mathematics) dtict Linear systems dtict Mathematics dtict Matrices(mathematics) dtict Numerical analysis) dtict Theoretical Mathematics scgdst Mathematik Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report 3 (DE-604)BV006665053 3 |
| spellingShingle | Givens, Wallace The linear equations problem Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report (Equations dtict Algorithms dtict Determinants(mathematics) dtict Linear systems dtict Mathematics dtict Matrices(mathematics) dtict Numerical analysis) dtict Theoretical Mathematics scgdst Mathematik |
| title | The linear equations problem |
| title_auth | The linear equations problem |
| title_exact_search | The linear equations problem |
| title_full | The linear equations problem |
| title_fullStr | The linear equations problem |
| title_full_unstemmed | The linear equations problem |
| title_short | The linear equations problem |
| title_sort | the linear equations problem |
| topic | (Equations dtict Algorithms dtict Determinants(mathematics) dtict Linear systems dtict Mathematics dtict Matrices(mathematics) dtict Numerical analysis) dtict Theoretical Mathematics scgdst Mathematik |
| topic_facet | (Equations Algorithms Determinants(mathematics) Linear systems Mathematics Matrices(mathematics) Numerical analysis) Theoretical Mathematics Mathematik |
| volume_link | (DE-604)BV006665053 |
| work_keys_str_mv | AT givenswallace thelinearequationsproblem |