جستجوی مقالات مرتبط با کلیدواژه
تکرار جستجوی کلیدواژه abs algorithms در نشریات گروه علوم پایه
abs algorithms
در نشریات گروه ریاضی
تکرار جستجوی کلیدواژه abs algorithms در مقالات مجلات علمی
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Iranian Journal of Numerical Analysis and Optimization, Volume:12 Issue: 2, Summer and Autumn 2022, PP 301 -314In 1984, Abaffy, Broyden, and Spediacto (ABS) introduced a class of the so-called ABS algorithms to solve systems of real linear equations. Later, the scaled ABS, the extended ABS, the block ABS, and the integer ABS algorithms were introduced leading to various well-known matrix factorizations. Here, we present a generalization of ABS algorithms containing all matrix factorizations such as triangular, W Z, and ZW . We discuss the octant interlocking factorization and make use of the generalized ABS algorithm as a more general approach for producing the octant interlocking factorization.Keywords: ABS algorithms, Quadrant interlocking factorization, Octant interlocking factorization
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Classes of Abaffy-Broyden-Spedicato (ABS) methods have been introduced for solving linear systems of equations. The algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes. Here, we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW factorizations of a nonsingular matrix as well as the $W^TW$ and $Z^TZ$ factorizations of a symmetric positives definite matrix. We also describe the QZ and the QW factorizations, with Q orthogonal, and show how to appropriate the parameters of the ABS algorithms to compute these factorizations.Keywords: ABS algorithms, WZ factorization, ZW factorizatio, WTW factorization, ZTZ factorization, QZ factoriation, QW factorization
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