Supremum & Stability of Weighted Pseudoinverses & Weighted Least Squares Problems Analysis & Computations Book

	Preface
Ch. 1	Introduction	1
1.1	Notation and definitions	1
1.2	Preliminaries	4
1.3	Basic mathematical background	11
1.4	Outline of the monograph	26
Ch. 2	WLS and WLSE problems	29
2.1	WLS	29
2.2	WLSE	34
2.3	Stability of pseudoinverses	44
2.4	Error estimates of WLS and WLSE	46
Ch. 3	Supremum of WP- and CWP-inverses	55
3.1	Supremum of WP-inverses	56
3.1.1	Supremum of WP-inverses over D	59
3.1.2	Supremum of WP-inverses over P	62
3.2	Supremum of CWP-inverses	66
3.2.1	Supremum of CWP-verses over D[subscript 2]	71
3.2.2	Supremum of CWP-inverses over P[subscript 2]	72
Ch. 4	Stability of WP-inverses and CWP-inverses	79
4.1	Stability of WP-inverses	79
4.2	Stability of CWP-inverses	85
Ch. 5	Perturbation bounds of W-projections	93
5.1	Only W is perturbed	95
5.2	Only A is perturbed	97
5.3	Both A and W are perturbed	100
5.4	When W [epsilon] P	102
Ch. 6	Upper error bounds of WLS and WLSE	105
6.1	Upper perturbation bounds of WLS	105
6.2	Upper perturbation bounds of WLSE	113
Ch. 7	Numerical computations of WLS	121
7.1	QRD	121
7.1.1	Householder transformations	122
7.1.2	Givens transformations	124
7.1.3	Householder and Givens column pivoting QRD	127
7.1.4	The MGS column pivoting QRD	129
7.2	LS by the QRD	132
7.3	Iterative refinement	134
7.4	Numerical computations of WLS	137
7.4.1	QRD for WLS	139
7.4.2	Weighted QR	141
7.4.3	Method based on Gaussian elimination	142
7.4.4	Nullspace-scaled hybrid algorithm	144
Ch. 8	Numerical computations of WLSE	145
8.1	Perturbation method	145
8.2	Method of weighting	147
8.3	Direct elimination methods	149
8.4	QRD based method	150
8.5	GSVD method	152
8.6	Numerical Examples	153
Ch. 9	Conclusion	157
	Bibliography	161
	Index	181