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Index Index

(Euclidean) length, Item
1-norm (vector), Item
1-norm, vector, Definition
2-norm (vector), Item
2-norm, matrix, Definition
2-norm, vector, Definition
\([ \cdot ] \), Remark
\(\epsilon_{\rm mach} \), Paragraph
\(\fl{ \cdot } \), Paragraph
\(\gamma_n \), Definition Definition
\(\infty \)-norm (vector), Item
\(\infty\)-norm, vector, Definition
\(\kappa(A)\), Definition Definition
\(\maxi( \cdot ) \), Paragraph
\(\overline A \), Definition
\(\overline x \), Paragraph
\(\overline {~~} \), Paragraph
\(\theta_j \), Lemma Lemma
\(\vert \cdot \vert \), Paragraph
\(e_j \), Paragraph
\(I \), Paragraph
\(p \)-norm (vector), Item
\(p\)-norm, matrix, Definition
\(p\)-norm, vector, Definition
absolute value, Subsection Paragraph Item
Alternative Computational Model, Subsubsection Paragraph
axpy, Paragraph
backward stable implementation, Definition
Basic Linear Algebra Subprograms, Subsection
BLAS, Subsection
blocked algorithm, Paragraph
catastrophic cancellation, Subsection
Cauchy-Schwarz inequality, Paragraph Theorem
characteristic polynomial, Subsection Definition
chasing the bulge, Paragraph
Cholesky decomposition, Week
Cholesky factor, Paragraph
Cholesky factorization, Paragraph Week
Cholesky factorization theorem, Theorem Theorem
Classical Gram-Schmidt, Subsection
complex conjugate, Paragraph
complex product, Item
conjugate, Paragraph Item
conjugate (of matrix), Item
conjugate (of vector), Item
conjugate of a matrix, Definition
conjugate transpose (of matrix), Item
conjugate transpose (of vector), Item
consistent matrix norm, Definition Definition Definition Definition
cost of basic linear algebra operations, Subsection
cubic convergence, Item Item
defective matrix, Paragraph Definition Definition
deflation, Subsection
descent methods, Week
determinant, Paragraph
direction of maximal magnification, Item
distance, Paragraph
dot product, Item Definition
eigenvalue, Definition Definition
eigenvector, Definition Definition
elementary elementary pivot matrix, Paragraph
equivalence style proof, Homework
Euclidean distance, Paragraph
exact descent method, Paragraph
fill-in, Paragraph
fixed-point equation, Paragraph
FLAME notation, Remark
floating point numbers, Subsection
forward substitution, Paragraph
Frobenius norm, Definition Item
Gauss transform, Subsection
Gaussian elimination, Section Subsection
Gaussian elimination with row exchanges, Subsection
Geometric multiplicity, Definition Definition
Givens' rotation, Subsection
gradient, Paragraph
Gram-Schmidt orthogonalization, Section
Hermitian, Definition
Hermitian Positive Definite, Item Subsection
Hermitian positive definite, Definition
Hermitian transpose, Remark Definition
Hermitian transpose (of matrix), Item
Hermitian transpose (of vector), Item
hessenberg matrix, Definition
homogeneity (of absolute value), Item
homogeneity (of matrix norm), Item Item
homogeneity (of vector norm), Item Item
Householder reflector, Definition Definition
Householder transformation, Paragraph Definition Definition
identity matrix, Paragraph
Implicit Q Theorem, Theorem
induced matrix norm, Subsection Definition
infinity norm, Paragraph
inner product, Item Definition
Jacobi algorithm (eigenvalues and vectors), Subsection
Jordan Canonical Form, Subsection
Krylov subspace, Definition Definition
left pseudo inverse, Definition
left pseudo-inverse, Paragraph
left singular vector, Theorem Theorem
Legendre polynomials, Paragraph
linear convergence, Definition Item Definition Item
linear least squares, Week
linear transformation, Subsection
LLS, Week
LU decomposition, Week Definition Paragraph Definition
LU factorization - existence, Theorem Theorem
LU factorization algorithm (bordered), Ponder This
LU factorization algorithm (left-looking), Paragraph
LU factorization algorithm (right-looking), Subsection
LU factorization with complete pivoting, Subsection
LU factorization with partial pivoting, Subsection
LU factorization with partial pivoting (right-looking algorithm), Subsection
LU factorization with pivoting, Section
magnitude, Paragraph
matrix 1-norm, Item
matrix 2-norm, Definition Item
matrix \(\infty \)-norm, Item
matrix \(p\)-norm, Definition
matrix norm, Definition Definition
matrix norm, 2-norm, Definition
matrix norm, \(p\)-norm, Definition
matrix norm, consistent, Definition Definition Definition Definition
matrix norm, Frobenius, Definition
matrix norm, induced, Subsection Definition
matrix norm, submultiplicative, Subsection Definition Definition
matrix norm, subordinate, Definition Definition
matrix p-norm, Item
matrix-vector multiplication, Paragraph
Method of Multiple Relatively Robust Representations (MRRR), Subsection
Method of Normal Equations, Paragraph
method of normal equations, Section
MRRR, Subsection
natural ordering, Item
nested dissection, Paragraph
norm, Week
norm, Frobenius, Definition
norm, infinity, Paragraph
norm, matrix, Definition Definition
norm, vector, Definition Definition
normal equations, Section Item
numerical stability, Week
orthogonal matrix, Remark
orthogonal projection, Paragraph
orthogonal vectors, Definition
orthonormal matrix, Definition
orthonormal vectors, Definition
over-relaxation, Paragraph
parent functions, Item
partial pivoting, Paragraph Subsection
pivot, Paragraph
pivot element, Paragraph
positive definite, Definition
positive definiteness (of absolute value), Item
positive defnitenessx (of matrix norm), Item Item
positive defnitenessx (of vector norm), Item Item
precondition, Item
principal leading submatrix, Definition Definition
pseudo inverse, Definition Paragraph
pseudo-inverse, Paragraph
QR algorithm, Subsection
QR decomposition, Week
QR Decomposition Theorem, Theorem Theorem
QR factorization, Week
QR factorization with column pivoting, Subsection Paragraph
quadratic convergence, Item Item
Rank-Revealing QR, Subsection
Rayleigh quotent, Definition Definition
Rayleigh Quotient Iteration, Subsection
residual, Homework
right pseudo inverse, Ponder This
right singular vector, Theorem Theorem
rotation, Subsubsection
rowl pivoting, Paragraph
RRQR, Subsection
Schur decomposition, Subsection Theorem Theorem
Schur Decomposition Theorem, Theorem Theorem
separator, Paragraph
shifted inverse power method, Subsection
shifted QR algorithm, Subsection
similarity transformation, Definition Definition
Singular Value Decomposition, Week Paragraph
singular vector, Theorem Theorem
solving triangular systems, Subsection
SOR, Paragraph
sparse linear system, Week
Spectral decomposition, Subsection
spectral decomposition, Theorem Theorem
Spectral Decomposition Theorem, Theorem Theorem
spectral radius, Definition Definition
stability, Week
standard basis vector, Definition Definition Definition Definition
Standard Computational Model, Subsubsection Paragraph
submultiplicative matrix norm, Subsection Definition Definition
subordinate matrix norm, Definition Definition
subspace iteration, Subsection Paragraph
successive over-relaxation, Paragraph
superlinear convergence, Item Item
superquadratic convergence, Item
symmetric positive definite, Definition Paragraph Definition
The Francis implicit QR Step, Subsection
The implicit Q theorem, Subsection
transpose, Definition
transpose (of matrix), Item
transpose (of vector), Item
triangle inequality (for absolute value)), Item
triangle inequality (for matrix norms)), Item Item
triangle inequality (for vector norms)), Item Item
triangular system, Subsection
Tridiagonal matrix, Definition
unit ball, Subsection Item
unit roundoff error, Paragraph
unitary matrix, Definition Definition
unitary similarity transformation, Definition Definition Definition
upper hessenberg matrix, Definition
Vandermonde matrix, Paragraph
vector 1-norm, Definition Item
vector 2-norm, Definition Item
vector \(\infty \)-norm, Item
vector \(\infty\)-norm, Definition
vector \(p \)-norm, Item
vector \(p\)-norm, Definition
vector norm, Definition Definition
vector norm, 1-norm, Definition
vector norm, 2-norm, Definition
vector norm, \(\infty\)-norm, Definition
vector norm, \(p\)-norm, Definition
Wilkinson shift, Item