See Gaussian elimination in All languages combined, or Wiktionary
{ "forms": [ { "form": "Gaussian eliminations", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "~" }, "expansion": "Gaussian elimination (countable and uncountable, plural Gaussian eliminations)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Russian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Linear algebra", "orig": "en:Linear algebra", "parents": [ "Algebra", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "text": "1976, Thomas E. Rosmond, Frank D. Faulkner, Direct Solution of Elliptic Equations by Block Cyclic Reduction and Factorization, Monthly Weather Review, Volume 104, Issues 1-6, American Meteorological Society, page 644,\nWe then repeat the Gaussian elimination procedure for the ( boldsymbol E-α₂⁽²⁾) factor in (35), obtaining another intermediate solution vector. It is immediately apparent in this example that four Gaussian eliminations are necessary to obtain ψ_(i,4)." }, { "ref": "1989, Richard A. Blech, “Parallel Gaussian Elimination of a Block Tridiagonal Matrix Using Multiple Microcomputers”, in Technical Report, NASA, page 1:", "text": "Theoretical partitioning and resource allocation for the Gaussian elimination method used to solve the matrix are discussed.", "type": "quote" }, { "ref": "1996, E. D'Hollander, G. R. Joubert, F. J. Peters, D. Trystram, Parallel Computing: State-of-the-art and Perspectives, Elsevier, page 642:", "text": "The use of Gaussian eliminations limits the range of functionality of the algorithm, which operates only with square matrices A.", "type": "quote" } ], "glosses": [ "A method of reducing an augmented matrix to row echelon form." ], "id": "en-Gaussian_elimination-en-noun-nFt~NcVr", "links": [ [ "linear algebra", "linear algebra" ], [ "augmented matrix", "augmented matrix" ], [ "row echelon form", "row echelon form" ] ], "raw_glosses": [ "(linear algebra) A method of reducing an augmented matrix to row echelon form." ], "related": [ { "word": "Cramer's rule" } ], "tags": [ "countable", "uncountable" ], "topics": [ "linear-algebra", "mathematics", "sciences" ], "translations": [ { "code": "fr", "lang": "French", "sense": "Gaussian elimination", "tags": [ "feminine" ], "word": "élimination de Gauss-Jordan" }, { "code": "fr", "lang": "French", "sense": "Gaussian elimination", "tags": [ "feminine" ], "word": "méthode du pivot de Gauss" }, { "code": "de", "lang": "German", "sense": "Gaussian elimination", "tags": [ "neuter" ], "word": "gaußsche Eliminationsverfahren" }, { "code": "de", "lang": "German", "sense": "Gaussian elimination", "tags": [ "neuter" ], "word": "Gauß-Verfahren" }, { "code": "it", "lang": "Italian", "sense": "Gaussian elimination", "tags": [ "masculine" ], "word": "metodo di eliminazione di Gauss" }, { "code": "it", "lang": "Italian", "sense": "Gaussian elimination", "tags": [ "masculine" ], "word": "MEG" }, { "code": "ru", "lang": "Russian", "roman": "métod Gáussa", "sense": "Gaussian elimination", "tags": [ "masculine" ], "word": "ме́тод Га́усса" }, { "code": "sv", "lang": "Swedish", "sense": "Gaussian elimination", "word": "Gausselimination" } ], "wikipedia": [ "Gaussian elimination" ] } ], "word": "Gaussian elimination" }
{ "forms": [ { "form": "Gaussian eliminations", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "~" }, "expansion": "Gaussian elimination (countable and uncountable, plural Gaussian eliminations)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "Cramer's rule" } ], "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English nouns", "English terms with quotations", "English uncountable nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with French translations", "Terms with German translations", "Terms with Italian translations", "Terms with Russian translations", "Terms with Swedish translations", "en:Linear algebra" ], "examples": [ { "text": "1976, Thomas E. Rosmond, Frank D. Faulkner, Direct Solution of Elliptic Equations by Block Cyclic Reduction and Factorization, Monthly Weather Review, Volume 104, Issues 1-6, American Meteorological Society, page 644,\nWe then repeat the Gaussian elimination procedure for the ( boldsymbol E-α₂⁽²⁾) factor in (35), obtaining another intermediate solution vector. It is immediately apparent in this example that four Gaussian eliminations are necessary to obtain ψ_(i,4)." }, { "ref": "1989, Richard A. Blech, “Parallel Gaussian Elimination of a Block Tridiagonal Matrix Using Multiple Microcomputers”, in Technical Report, NASA, page 1:", "text": "Theoretical partitioning and resource allocation for the Gaussian elimination method used to solve the matrix are discussed.", "type": "quote" }, { "ref": "1996, E. D'Hollander, G. R. Joubert, F. J. Peters, D. Trystram, Parallel Computing: State-of-the-art and Perspectives, Elsevier, page 642:", "text": "The use of Gaussian eliminations limits the range of functionality of the algorithm, which operates only with square matrices A.", "type": "quote" } ], "glosses": [ "A method of reducing an augmented matrix to row echelon form." ], "links": [ [ "linear algebra", "linear algebra" ], [ "augmented matrix", "augmented matrix" ], [ "row echelon form", "row echelon form" ] ], "raw_glosses": [ "(linear algebra) A method of reducing an augmented matrix to row echelon form." ], "tags": [ "countable", "uncountable" ], "topics": [ "linear-algebra", "mathematics", "sciences" ], "wikipedia": [ "Gaussian elimination" ] } ], "translations": [ { "code": "fr", "lang": "French", "sense": "Gaussian elimination", "tags": [ "feminine" ], "word": "élimination de Gauss-Jordan" }, { "code": "fr", "lang": "French", "sense": "Gaussian elimination", "tags": [ "feminine" ], "word": "méthode du pivot de Gauss" }, { "code": "de", "lang": "German", "sense": "Gaussian elimination", "tags": [ "neuter" ], "word": "gaußsche Eliminationsverfahren" }, { "code": "de", "lang": "German", "sense": "Gaussian elimination", "tags": [ "neuter" ], "word": "Gauß-Verfahren" }, { "code": "it", "lang": "Italian", "sense": "Gaussian elimination", "tags": [ "masculine" ], "word": "metodo di eliminazione di Gauss" }, { "code": "it", "lang": "Italian", "sense": "Gaussian elimination", "tags": [ "masculine" ], "word": "MEG" }, { "code": "ru", "lang": "Russian", "roman": "métod Gáussa", "sense": "Gaussian elimination", "tags": [ "masculine" ], "word": "ме́тод Га́усса" }, { "code": "sv", "lang": "Swedish", "sense": "Gaussian elimination", "word": "Gausselimination" } ], "word": "Gaussian elimination" }
Download raw JSONL data for Gaussian elimination meaning in English (3.4kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.