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This book is devoted to the latest advances in the area of electrothermal modelling of electronic components and networks. It contains eight sections by different teams of authors. These sections contain the results of: (a) electro-thermal simulations of SiC power MOSFETs using a SPICE-like simulation program; (b) modelling thermal properties of inductors taking into account the influence of the core volume on the efficiency of heat removal; (c) investigations into the problem of inserting a temperature sensor in the neighbourhood of a chip to monitor its junction temperature; (d) computations of the internal temperature of power LEDs situated in modules containing multiple-power LEDs, taking into account both self-heating in each power LED and mutual thermal couplings between each diode; (e) analyses of DC-DC converters using the electrothermal averaged model of the diode–transistor switch, including an IGBT and a rapid-switching diode; (f) electrothermal modelling of SiC power BJTs; (g) analysis of the efficiency of selected algorithms used for solving heat transfer problems at nanoscale; (h) analysis related to thermal simulation of the test structure dedicated to heat-diffusion investigation at the nanoscale.

Dual-Phase-Lag heat transfer model --- thermal simulation algorithm --- thermal measurements --- Finite Difference Method scheme --- Grünwald–Letnikov fractional derivative --- Krylov subspace-based model order reduction --- algorithm efficiency analysis --- relative error analysis --- algorithm convergence analysis --- computational complexity analysis --- finite difference method scheme --- BJT --- modelling --- self-heating --- silicon carbide --- SPICE --- IGBT --- DC–DC converter --- electrothermal model --- averaged model --- thermal phenomena --- diode–transistor switch --- power electronics --- multi-LED lighting modules --- device thermal coupling --- compact thermal models --- temperature sensors --- microprocessor --- throughput improvement --- inductors --- ferromagnetic cores --- thermal model --- transient thermal impedance --- thermal resistance --- electrothermal (ET) simulation --- finite-element method (FEM) --- model-order reduction (MOR) --- multicellular power MOSFET --- silicon carbide (SiC)

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This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

Matrices. --- Numerical analysis. --- Mathematical analysis --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Matrices --- Numerical analysis --- Algorithm. --- Analysis of algorithms. --- Analytic function. --- Asymptotic analysis. --- Basis (linear algebra). --- Basis function. --- Biconjugate gradient method. --- Bidiagonal matrix. --- Bilinear form. --- Calculation. --- Characteristic polynomial. --- Chebyshev polynomials. --- Coefficient. --- Complex number. --- Computation. --- Condition number. --- Conjugate gradient method. --- Conjugate transpose. --- Cross-validation (statistics). --- Curve fitting. --- Degeneracy (mathematics). --- Determinant. --- Diagonal matrix. --- Dimension (vector space). --- Eigenvalues and eigenvectors. --- Equation. --- Estimation. --- Estimator. --- Exponential function. --- Factorization. --- Function (mathematics). --- Function of a real variable. --- Functional analysis. --- Gaussian quadrature. --- Hankel matrix. --- Hermite interpolation. --- Hessenberg matrix. --- Hilbert matrix. --- Holomorphic function. --- Identity matrix. --- Interlacing (bitmaps). --- Inverse iteration. --- Inverse problem. --- Invertible matrix. --- Iteration. --- Iterative method. --- Jacobi matrix. --- Krylov subspace. --- Laguerre polynomials. --- Lanczos algorithm. --- Linear differential equation. --- Linear regression. --- Linear subspace. --- Logarithm. --- Machine epsilon. --- Matrix function. --- Matrix polynomial. --- Maxima and minima. --- Mean value theorem. --- Meromorphic function. --- Moment (mathematics). --- Moment matrix. --- Moment problem. --- Monic polynomial. --- Monomial. --- Monotonic function. --- Newton's method. --- Numerical integration. --- Numerical linear algebra. --- Orthogonal basis. --- Orthogonal matrix. --- Orthogonal polynomials. --- Orthogonal transformation. --- Orthogonality. --- Orthogonalization. --- Orthonormal basis. --- Partial fraction decomposition. --- Polynomial. --- Preconditioner. --- QR algorithm. --- QR decomposition. --- Quadratic form. --- Rate of convergence. --- Recurrence relation. --- Regularization (mathematics). --- Rotation matrix. --- Singular value. --- Square (algebra). --- Summation. --- Symmetric matrix. --- Theorem. --- Tikhonov regularization. --- Trace (linear algebra). --- Triangular matrix. --- Tridiagonal matrix. --- Upper and lower bounds. --- Variable (mathematics). --- Vector space. --- Weight function.