MATH 685/ CSI 700/ OR 682 Lecture Notes Lecture 4. Least squares
Method of least squares Measurement errors are inevitable in observational and experimental sciences
Errors can be smoothed out by averaging over many cases, i.e., taking more measurements than are strictly necessary to determine parameters of system Resulting system is overdetermined, so usually there is no exact
solution In effect, higher dimensional data are projected into lower dimensional space to suppress irrelevant detail Such projection is most conveniently accomplished by
method of least squares Linear least squares
Data fitting Data fitting
Normal Equations Orthogonality
Orthogonality Orthogonal Projector
Pseudoinverse Sensitivity and Conditioning
Sensitivity and Conditioning Solving normal equations
Shortcomings Augmented system method
Augmented system method Orthogonal Transformations
Triangular Least Squares Triangular Least Squares
QR Factorization Orthogonal Bases
Computing QR factorization To compute QR factorization of m n matrix A, with m > n, we
annihilate subdiagonal entries of successive columns of A, eventually reaching upper triangular form
Similar to LU factorization by Gaussian elimination, but use orthogonal transformations instead of elementary elimination matrices
Congress takes time to pass legislation. Operational Lag-Spending/planning takes time to organize and execute ( changing taxing is quicker) Politically Motivated Policies. Politicians may use economically inappropriate policies to get reelected. Ex: A senator promises more welfare and public works...
TRAINING FACULTY AND STAFF ON FERPA ADAPTED FROM AACRAO FEDERAL COMPLIANCE COMMITTEE FOR EAST STROUDSBURG UNIVERSITY * * The answer to e. is: Any release of non-directory information made to a third party who is not a school official.
For example, a person's eyes can often convey a far more vivid message than words can often do . Complementing: they may add to or complement a verbal message. A boss who pats a person on the back in addition...
Placement of Aeroneb with HFOV Jim Fink, PhD, RRT, FAARC [email protected] High Frequency Oscillation Ventilation : In Vitro Setup Infant Ventilation Demers et al. ATS San Diego, 2005 Aerosol Deposition 10.25±6.0% Effect of Nebulizer Position on Aerosol Delivery with HFOV...
His hands were warm and small and knowleadgeable.When I saw them again last night, they were two ferrets,Playing all by themselves in a moonlit field. by . Seamus Heaney. To get into the poetic spirit, let's read this short poem…...
Physics 10 MONDAY APRIL 14th physics behind the knuckleball ... McGraw Hill Ryerson 2007 ACTIVITY: In a group of three complete the Slow Motion and Fast Motion Trial Lab on Page 358 of your text book. Complete the lab using...