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"Summary:This monograph provides a systematic treatment of the abstract theory of adjoint semigroups. Following a presentation of the basic elementary results, the text discusses such topics as interpolation and extrapolation, weak-continuous semigroups and Hille-Yosida operators"

"ABTSRAKBeberapa permasalahan analisis numerik dapat disederhanakan menjadi permasalahan penyelesaian sistem persamaan linear AOC=b,dengan A?Am'a, xeRn, dan beRm. Untuk man, permasalahan persamaan ini merupakan permasalahan kuadrat terkecil yang mencari penyelesaian x dengan meminimumkan norm residu ||Ax-b|| Penelitian ini membahas sistem persamaan linear Toeplitz T. Metode-metode yang dipakai untuk menyelesaikan sistem persamaan linear ini adalah faktorisasi Cholesky, eliminasi Gauss, Conjugate Gradient, faktorisasi fast inverse QR, dan faktorisasi fast QR. Penelitian ini bertujuan untuk melihat efisiensi waktu proses dan keakuratan antara penyelesaian numerik yang diperoleh dengan penyelesaian eksak. Hasil percobaan menunjukkan bahwa metode-metode tersebut dapat dipakai untuk menyelesaikan persamaan linear dengan matriks T well-condition. Bila menggunakan matriks Toeplitz T ill-condition, maka metode Cholesky kurang akurat dibandingkan dengan keempat metode lainnya. Solusi paling cepat dan paling akurat dihasilkan oleh metode faktorisasi Fast QR."

"Don't let the title fool you! If you are interested in numerical analysis, applied mathematics, or the solution procedures for differential equations, you will find this book useful. Because of Lanczos' unique style of describing mathematical facts in nonmathematical language, Linear Differential Operators also will be helpful to nonmathematicians interested in applying the methods and techniques described. Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems. Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: "What are the basic and characteristic properties of linear differential operators?" In the author's words, this book is written for those "to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field.""

"Inversi seismik telah diaplikasikan untuk membantu proses interpretasi data seismik dengan menghasilkan parameter impedansi akustik yang dapat berguna dalam karakterisasi suatu reservoar hidrokarbon. Beberapa metode yang dapat digunakan untuk melakukan inversi seismik antara lain : BLIMP (Bandlimited Impedance Inversion), Model Based Inversion dan Sparse Spike Inversion. Pada kasus ini dibandingkan dua buah metode antara bandlimited inversion dan linear programming sparse spike inversion. Metode bandlimited menggunakan deret tras seismik sebagai koefisien refleksi untuk kemudian dilakukan penambahan low frequency trend dari data impedansi sumur kepada setiap tras seismik. Sedangkan untuk metode linear programming sparse spike inversion mempergunakan deret reflektivitas hasil proses dekonvolusi yang masih bersifat bandlimited diolah dengan metode pemograman linier untuk menghasilkan deret reflektifitas yang sparse spike. Linear programming sparse spike inversion menunjukkan hasil impedansi akustik dengan karakteristik yang blocky sedangkan metode bandlimited menghasilkan impedansi akustik dengan karakter smooth menyerupai tras seismik. Linear programming sparse spike memiliki daya pisah yang lebih baik dibandingkan metode bandlimited tampak dari keberhasilan metode ini menunjukkan kemungkinan adanya patahan pada zona target yang tidak dapat ditunjukkan oleh metode bandlimited.

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Seismic inversion method has been aplied to the interpretation of seismic data and has been succed for maping acoustic impedance distribution which is useful for reservoir caracterization. There are at least three methods of post stack seismic inversion, Band Limited Impedance Inversion, Model Based Inversion and Sparse Spike Inversion. In this study it has been compared two inversion methods between bandlimited inversion and linear programming sparse spike inversion. Bandlimited inversion method use seismic trace as series of reflection coefficient then added low frequency trend of acoustic impedance from well to each seismic trace. The other side linear programming sparse spike inversion use linear programming algorithm for producing sparse spike reflection coefficient. Linear programming sparse spike inversion result acoustic impedance with blocky structure and the other hand bandlimited show smooth structure like seismic trace. Linear programming sparse spike inversion has better resolution than bandlimited inversion, linear programming sparse spike inversion could show existence of fault in target zone which bandlimited failed to show it."