| CONDITION NUMBERS, ITERATIVE REFINEMENT AND ERROR BOUNDS |
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| 引用本文： | JOHNH.KALIVAS,PATRICK LANG. CONDITION NUMBERS, ITERATIVE REFINEMENT AND ERROR BOUNDS[J]. 地理学报(英文版), 1989, 0(1) |
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| 作者姓名： | JOHNH.KALIVAS PATRICK LANG |
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| 作者单位： | Department of Chemistry Idaho State University Pocatello Idaho 83209 U.S.A.，Department of Mathematics Idaho State University Pocatello Idaho 83209 U.S.A. |
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| 摘 要： | Concentration estimates of components present in a sample mixture can be obtained using matrixmathematics. In the past, the condition number of the calibration matrix has been used to give anamplification factor by which uncertainties in data can work through to errors in the concentrationestimates. This paper explores an additional interpretation of condition numbers with regards tosignificant figures and rounding errors. A procedure is suggested which will always give the most accurateconcentration estimates provided the calibration matrix is not too ill-conditioned. Condition numbershave also been used by analytical chemists to discuss the error bounds for concentration estimates.Unfortunately, only one representative error bound can be approximated for all the components. Thispaper will show how to compute bounds for individual concentration estimates obtained as solutions to asystem of m equations and n unknowns. The procedure is appropriate when calibration data and sampleresponses are inaccurate.
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CONDITION NUMBERS, ITERATIVE REFINEMENT AND ERROR BOUNDS |
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| JOHN H. KALIVAS. CONDITION NUMBERS, ITERATIVE REFINEMENT AND ERROR BOUNDS[J]. Journal of Geographical Sciences, 1989, 0(1) |
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| Authors: | JOHN H. KALIVAS |
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| Affiliation: | JOHN H. KALIVAS,Department of Chemistry,Idaho State University,Pocatello,Idaho,U.S.A. PATRICK LANG,Department of Mathematics,Idaho State University,Pocatello,Idaho,U.S.A. |
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| Abstract: | Concentration estimates of components present in a sample mixture can be obtained using matrix mathematics. In the past, the condition number of the calibration matrix has been used to give an amplification factor by which uncertainties in data can work through to errors in the concentration estimates. This paper explores an additional interpretation of condition numbers with regards to significant figures and rounding errors. A procedure is suggested which will always give the most accurate concentration estimates provided the calibration matrix is not too ill-conditioned. Condition numbers have also been used by analytical chemists to discuss the error bounds for concentration estimates. Unfortunately, only one representative error bound can be approximated for all the components. This paper will show how to compute bounds for individual concentration estimates obtained as solutions to a system of m equations and n unknowns. The procedure is appropriate when calibration data and sample responses are inaccurate. |
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| Keywords: | Multicomponent analysis Iterative refinement Simplex method Condition numbers Linear programming |
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